-
Notifications
You must be signed in to change notification settings - Fork 2
Expand file tree
/
Copy pathdynamical_systems_fixed.html
More file actions
2547 lines (2304 loc) · 116 KB
/
Copy pathdynamical_systems_fixed.html
File metadata and controls
2547 lines (2304 loc) · 116 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Dynamical Systems & Chaos Masterclass</title>
<style>
:root {
--chaos-red: #ff2d55;
--attractor-cyan: #00f5ff;
--bifur-green: #39ff14;
--phase-purple: #bf5fff;
--lyap-orange: #ff6b35;
--strange-gold: #ffd700;
--dark-bg: #030108;
--card-bg: #07030f;
--card-border: #130828;
--text-primary: #f0e8ff;
--text-secondary: #7766aa;
--text-dim: #2a1a44;
}
* { margin:0; padding:0; box-sizing:border-box; }
body {
background: var(--dark-bg);
color: var(--text-primary);
font-family: 'Segoe UI', system-ui, sans-serif;
overflow-x: hidden;
min-height: 100vh;
}
#bg-canvas {
position: fixed; inset: 0; z-index: 0; pointer-events: none;
}
header {
position: relative; z-index: 10;
text-align: center; padding: 55px 20px 35px;
}
.hero-badge {
display: inline-flex; align-items: center; gap: 8px;
font-size: 11px; letter-spacing: 4px; text-transform: uppercase;
color: var(--chaos-red);
border: 1px solid var(--chaos-red);
padding: 5px 20px; border-radius: 20px; margin-bottom: 20px;
animation: badge-chaos 3s ease-in-out infinite;
}
@keyframes badge-chaos {
0%,100% { box-shadow: 0 0 8px var(--chaos-red); }
33% { box-shadow: 0 0 20px var(--attractor-cyan), 0 0 40px rgba(0,245,255,0.2); border-color: var(--attractor-cyan); color: var(--attractor-cyan); }
66% { box-shadow: 0 0 20px var(--bifur-green), 0 0 40px rgba(57,255,20,0.2); border-color: var(--bifur-green); color: var(--bifur-green); }
}
h1.main-title {
font-size: clamp(2rem, 5.5vw, 4.8rem);
font-weight: 900; line-height: 1.08;
background: linear-gradient(135deg, var(--attractor-cyan), var(--phase-purple), var(--chaos-red), var(--strange-gold));
-webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text;
filter: drop-shadow(0 0 35px rgba(191,95,255,0.5));
margin-bottom: 16px;
}
.subtitle {
font-size: 1rem; color: var(--text-secondary);
max-width: 700px; margin: 0 auto 28px; line-height: 1.8;
}
.nav-pills {
display: flex; justify-content: center; gap: 8px; flex-wrap: wrap;
}
.nav-pill {
padding: 6px 16px; border-radius: 20px; font-size: 11px; font-weight: 700;
letter-spacing: 1px; cursor: pointer; transition: all 0.3s; border: 1px solid;
background: none;
}
.np1 { border-color: var(--attractor-cyan); color: var(--attractor-cyan); background: rgba(0,245,255,0.06); }
.np2 { border-color: var(--chaos-red); color: var(--chaos-red); background: rgba(255,45,85,0.06); }
.np3 { border-color: var(--bifur-green); color: var(--bifur-green); background: rgba(57,255,20,0.06); }
.np4 { border-color: var(--phase-purple); color: var(--phase-purple); background: rgba(191,95,255,0.06); }
.np5 { border-color: var(--strange-gold); color: var(--strange-gold); background: rgba(255,215,0,0.06); }
.nav-pill:hover { transform: translateY(-2px); filter: brightness(1.5); }
.hero-wrap {
position: relative; z-index: 5;
max-width: 1200px; margin: 0 auto; padding: 0 20px;
}
.hero-header {
display: flex; align-items: center; gap: 14px; margin-bottom: 12px; flex-wrap: wrap;
}
.hero-title-block { flex: 1; }
.hero-title-block h2 { font-size: 1.1rem; font-weight: 800; color: var(--attractor-cyan); }
.hero-title-block p { font-size: 0.8rem; color: var(--text-secondary); margin-top: 3px; }
.hero-controls {
display: flex; gap: 8px; flex-wrap: wrap; align-items: center;
}
.hc-btn {
padding: 6px 14px; border-radius: 8px; font-size: 11px; font-weight: 700;
letter-spacing: 1px; cursor: pointer; transition: all 0.25s; border: 1px solid;
background: none;
}
.hcb1 { border-color: var(--attractor-cyan); color: var(--attractor-cyan); }
.hcb2 { border-color: var(--chaos-red); color: var(--chaos-red); }
.hcb3 { border-color: var(--bifur-green); color: var(--bifur-green); }
.hcb4 { border-color: var(--phase-purple); color: var(--phase-purple); }
.hcb5 { border-color: var(--text-dim); color: var(--text-secondary); }
.hc-btn:hover { transform: translateY(-1px); filter: brightness(1.5); }
.hcb1:hover { background: rgba(0,245,255,0.1); }
.hcb2:hover { background: rgba(255,45,85,0.1); }
.hcb3:hover { background: rgba(57,255,20,0.1); }
.hcb4:hover { background: rgba(191,95,255,0.1); }
.hero-canvas-wrap {
position: relative; border-radius: 16px; overflow: hidden;
border: 1px solid var(--card-border);
box-shadow: 0 0 80px rgba(191,95,255,0.08), inset 0 0 80px rgba(0,0,0,0.6);
}
#lorenzCanvas { display: block; width: 100%; background: #030108; cursor: grab; }
#lorenzCanvas:active { cursor: grabbing; }
.hero-overlay {
position: absolute; top: 14px; left: 14px;
display: flex; flex-direction: column; gap: 6px; pointer-events: none;
}
.ov-chip {
background: rgba(3,1,8,0.88); border: 1px solid var(--card-border);
border-radius: 8px; padding: 6px 11px;
font-size: 10px; font-family: 'Courier New', monospace;
color: var(--text-secondary); line-height: 1.7;
}
.ov-chip span { color: var(--attractor-cyan); }
.ov-chip .lyap-pos { color: var(--chaos-red); }
.ov-chip .lyap-neg { color: var(--bifur-green); }
.hero-sys-badge {
position: absolute; top: 14px; right: 14px;
background: rgba(3,1,8,0.9); border-radius: 10px;
padding: 8px 14px; font-size: 11px; font-weight: 700;
letter-spacing: 1px; pointer-events: none; color: var(--attractor-cyan);
}
.hint-bar {
text-align: center; font-size: 11px; color: var(--text-dim);
margin-top: 8px; letter-spacing: 0.5px;
}
.param-panel {
display: flex; gap: 12px; flex-wrap: wrap; margin-top: 12px;
background: rgba(0,0,0,0.4); border: 1px solid var(--card-border);
border-radius: 12px; padding: 14px 18px;
}
.param-group { display: flex; flex-direction: column; gap: 4px; flex: 1; min-width: 120px; }
.param-label { font-size: 10px; color: var(--text-secondary); letter-spacing: 1px; font-family: 'Courier New', monospace; }
input[type=range] {
-webkit-appearance: none; appearance: none;
width: 100%; height: 3px; border-radius: 2px;
background: var(--card-border); outline: none;
cursor: pointer;
}
input[type=range]::-webkit-slider-thumb {
-webkit-appearance: none; width: 14px; height: 14px;
border-radius: 50%; background: var(--attractor-cyan);
box-shadow: 0 0 8px var(--attractor-cyan); cursor: pointer;
}
.param-val { font-size: 11px; color: var(--attractor-cyan); font-family: 'Courier New', monospace; }
.main-container {
position: relative; z-index: 5;
max-width: 1200px; margin: 0 auto; padding: 10px 20px;
}
.stats-bar {
display: grid; grid-template-columns: repeat(auto-fit, minmax(130px,1fr));
gap: 14px; margin: 28px 0;
}
.stat-item {
text-align: center; padding: 18px 12px;
background: var(--card-bg); border: 1px solid var(--card-border);
border-radius: 12px; transition: all 0.3s; cursor: default;
}
.stat-item:hover { border-color: var(--phase-purple); transform: translateY(-2px); }
.stat-item .num {
font-size: 2rem; font-weight: 900; line-height: 1;
background: linear-gradient(135deg, var(--attractor-cyan), var(--phase-purple));
-webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text;
margin-bottom: 5px;
}
.stat-item .lbl { font-size: 0.7rem; color: var(--text-dim); text-transform: uppercase; letter-spacing: 1px; }
.sec-header {
display: flex; align-items: center; gap: 14px; margin: 46px 0 20px; flex-wrap: wrap;
}
.sec-icon {
width: 48px; height: 48px; border-radius: 12px;
display: flex; align-items: center; justify-content: center;
font-size: 22px; flex-shrink: 0;
}
.si-cyan { background: rgba(0,245,255,0.12); box-shadow: 0 0 18px rgba(0,245,255,0.18); }
.si-red { background: rgba(255,45,85,0.12); box-shadow: 0 0 18px rgba(255,45,85,0.18); }
.si-green { background: rgba(57,255,20,0.12); box-shadow: 0 0 18px rgba(57,255,20,0.18); }
.si-purple { background: rgba(191,95,255,0.12); box-shadow: 0 0 18px rgba(191,95,255,0.18); }
.si-gold { background: rgba(255,215,0,0.12); box-shadow: 0 0 18px rgba(255,215,0,0.18); }
.si-orange { background: rgba(255,107,53,0.12); box-shadow: 0 0 18px rgba(255,107,53,0.18); }
.sec-title-grp h2 { font-size: 1.5rem; font-weight: 800; }
.sec-title-grp p { font-size: 0.81rem; color: var(--text-secondary); margin-top: 3px; }
.sec-badge {
margin-left: auto; font-size: 10px; letter-spacing: 2px;
text-transform: uppercase; padding: 4px 12px; border-radius: 10px;
font-weight: 700; white-space: nowrap;
}
.card-grid { display: grid; gap: 16px; }
.grid-2 { grid-template-columns: repeat(auto-fill, minmax(350px,1fr)); }
.grid-3 { grid-template-columns: repeat(auto-fill, minmax(285px,1fr)); }
.grid-4 { grid-template-columns: repeat(auto-fill, minmax(240px,1fr)); }
.card {
background: var(--card-bg); border: 1px solid var(--card-border);
border-radius: 14px; padding: 20px; position: relative; overflow: hidden;
cursor: pointer; transition: all 0.3s cubic-bezier(0.4,0,0.2,1);
}
.card::before {
content: ''; position: absolute; top: 0; left: 0; right: 0; height: 2px;
background: var(--acc, var(--attractor-cyan));
transform: scaleX(0); transition: transform 0.3s; transform-origin: left;
}
.card:hover { transform: translateY(-4px); }
.card:hover::before { transform: scaleX(1); }
.card:hover { box-shadow: 0 8px 40px rgba(0,0,0,0.5), 0 0 0 1px var(--acc, var(--attractor-cyan)) inset; }
.cc { --acc: var(--attractor-cyan); }
.cr { --acc: var(--chaos-red); }
.cg { --acc: var(--bifur-green); }
.cp { --acc: var(--phase-purple); }
.co { --acc: var(--lyap-orange); }
.ck { --acc: var(--strange-gold); }
.card-glow {
position: absolute; top: -40px; right: -40px;
width: 110px; height: 110px; border-radius: 50%;
background: var(--acc, var(--attractor-cyan));
opacity: 0.04; filter: blur(28px); transition: opacity 0.3s;
}
.card:hover .card-glow { opacity: 0.15; }
.card-num {
font-size: 10px; font-weight: 700; letter-spacing: 2px;
color: var(--acc, var(--attractor-cyan));
margin-bottom: 9px; display: flex; align-items: center; gap: 8px;
}
.card-num::after {
content: ''; flex: 1; height: 1px;
background: var(--acc); opacity: 0.25;
}
.card h3 { font-size: 0.96rem; font-weight: 700; margin-bottom: 7px; line-height: 1.35; }
.card p { font-size: 0.8rem; color: var(--text-secondary); line-height: 1.65; margin-bottom: 12px; }
.card-mini { width: 100%; height: 88px; border-radius: 8px; overflow: hidden; margin-bottom: 12px; background: rgba(0,0,0,0.5); }
.card-mini canvas { width: 100%; height: 100%; display: block; }
.card-tags { display: flex; flex-wrap: wrap; gap: 5px; margin-bottom: 12px; }
.tag {
font-size: 9px; padding: 2px 7px; border-radius: 5px;
background: rgba(255,255,255,0.04); color: var(--text-secondary);
border: 1px solid var(--card-border); letter-spacing: 0.5px;
}
.card-footer { display: flex; align-items: center; justify-content: space-between; }
.duration { font-size: 10px; color: var(--text-dim); }
.diff-dots { display: flex; gap: 3px; }
.dot { width: 6px; height: 6px; border-radius: 50%; background: var(--card-border); }
.dot.f { background: var(--acc); }
.feat-card {
grid-column: 1 / -1;
display: grid; grid-template-columns: 1fr 340px; overflow: hidden; min-height: 210px;
}
.feat-card .card-content { padding: 24px; }
.feat-card canvas { width: 100%; height: 100%; display: block; }
@media(max-width:680px){
.feat-card { grid-template-columns: 1fr; }
.feat-card canvas { height: 140px; }
}
.bifur-wrap {
background: rgba(0,0,0,0.5); border: 1px solid var(--card-border);
border-radius: 16px; overflow: hidden; margin: 24px 0;
}
.bifur-header {
display: flex; align-items: center; gap: 12px; padding: 16px 20px;
border-bottom: 1px solid var(--card-border); flex-wrap: wrap;
}
.bifur-header h3 { font-size: 1rem; font-weight: 800; color: var(--bifur-green); }
.bifur-header p { font-size: 0.78rem; color: var(--text-secondary); margin-top: 2px; }
#bifurCanvas { display: block; width: 100%; cursor: crosshair; }
.bifur-controls {
display: flex; gap: 10px; flex-wrap: wrap; padding: 14px 20px;
border-top: 1px solid var(--card-border); align-items: center;
}
.bifur-stat {
font-size: 11px; color: var(--bifur-green);
font-family: 'Courier New', monospace;
background: rgba(57,255,20,0.05); border: 1px solid rgba(57,255,20,0.2);
padding: 5px 12px; border-radius: 8px;
}
.demo-panel {
background: rgba(0,0,0,0.4); border: 1px solid var(--card-border);
border-radius: 14px; overflow: hidden; margin: 24px 0;
}
.demo-tabs {
display: flex; overflow-x: auto; background: rgba(0,0,0,0.3);
border-bottom: 1px solid var(--card-border);
}
.demo-tab {
padding: 11px 18px; font-size: 11px; font-weight: 700;
letter-spacing: 1px; color: var(--text-dim); cursor: pointer;
border-bottom: 2px solid transparent; transition: all 0.3s;
white-space: nowrap; background: none;
border-top: none; border-left: none; border-right: none;
}
.demo-tab.active { color: var(--attractor-cyan); border-bottom-color: var(--attractor-cyan); background: rgba(0,245,255,0.05); }
.demo-tab:hover:not(.active) { color: var(--text-secondary); }
.demo-content { padding: 22px; display: none; }
.demo-content.active { display: block; }
.demo-2col { display: grid; grid-template-columns: 1fr 1fr; gap: 20px; align-items: start; }
@media(max-width:640px) { .demo-2col { grid-template-columns: 1fr; } }
.demo-2col canvas { width: 100%; border-radius: 10px; display: block; background: rgba(0,0,0,0.6); }
.demo-explain h4 { font-size: 0.93rem; font-weight: 700; margin-bottom: 9px; color: var(--attractor-cyan); }
.demo-explain p { font-size: 0.81rem; color: var(--text-secondary); line-height: 1.7; margin-bottom: 11px; }
.code-block {
background: rgba(0,0,0,0.7); border: 1px solid var(--card-border);
border-radius: 8px; padding: 12px; font-family: 'Courier New', monospace;
font-size: 10.5px; color: var(--bifur-green); overflow-x: auto; line-height: 1.7;
}
.code-block .kw { color: var(--phase-purple); }
.code-block .num { color: var(--lyap-orange); }
.code-block .cm { color: #4a3a6a; }
.code-block .hl { color: var(--attractor-cyan); }
.insight-box {
background: linear-gradient(135deg, rgba(0,0,0,0.7), rgba(10,0,20,0.7));
border: 1px solid rgba(191,95,255,0.3); border-radius: 12px;
padding: 18px 22px; margin: 22px 0; position: relative; overflow: hidden;
}
.insight-box.red { border-color: rgba(255,45,85,0.3); }
.insight-box.green { border-color: rgba(57,255,20,0.3); }
.insight-box.gold { border-color: rgba(255,215,0,0.3); }
.insight-box.orange { border-color: rgba(255,107,53,0.3); }
.insight-box::after {
content: ''; position: absolute; top: 0; right: 0; bottom: 0;
width: 3px; background: var(--ib-col, var(--phase-purple));
box-shadow: 0 0 12px var(--ib-col, var(--phase-purple));
}
.insight-box h4 {
font-size: 0.75rem; letter-spacing: 2px; text-transform: uppercase;
color: var(--phase-purple); margin-bottom: 8px;
}
.insight-box.red h4 { color: var(--chaos-red); }
.insight-box.green h4 { color: var(--bifur-green); }
.insight-box.gold h4 { color: var(--strange-gold); }
.insight-box.orange h4 { color: var(--lyap-orange); }
.insight-box p { font-size: 0.87rem; color: var(--text-secondary); line-height: 1.75; }
/* ── KEY INSIGHT (new — practical takeaway blocks) ── */
.key-insight {
display: grid; grid-template-columns: auto 1fr; gap: 14px;
background: rgba(0,245,255,0.03); border: 1px solid rgba(0,245,255,0.15);
border-radius: 10px; padding: 14px 18px; margin: 14px 0;
}
.ki-icon { font-size: 22px; margin-top: 2px; }
.ki-body h5 { font-size: 0.78rem; font-weight: 700; color: var(--attractor-cyan); margin-bottom: 4px; letter-spacing: 1px; text-transform: uppercase; }
.ki-body p { font-size: 0.8rem; color: var(--text-secondary); line-height: 1.65; }
.key-insight.red { border-color: rgba(255,45,85,0.2); background: rgba(255,45,85,0.03); }
.key-insight.red .ki-body h5 { color: var(--chaos-red); }
.key-insight.green { border-color: rgba(57,255,20,0.2); background: rgba(57,255,20,0.03); }
.key-insight.green .ki-body h5 { color: var(--bifur-green); }
.key-insight.gold { border-color: rgba(255,215,0,0.2); background: rgba(255,215,0,0.03); }
.key-insight.gold .ki-body h5 { color: var(--strange-gold); }
.formula-strip {
display: flex; gap: 10px; overflow-x: auto; padding: 10px 0;
scrollbar-width: thin; scrollbar-color: var(--phase-purple) transparent;
}
.formula-chip {
flex-shrink: 0; background: rgba(191,95,255,0.05);
border: 1px solid rgba(191,95,255,0.2); border-radius: 9px;
padding: 9px 14px; font-family: 'Courier New', monospace;
font-size: 12px; color: var(--phase-purple); white-space: nowrap;
transition: all 0.3s; cursor: default;
}
.formula-chip:hover {
background: rgba(191,95,255,0.12); transform: translateY(-2px);
box-shadow: 0 4px 18px rgba(191,95,255,0.2);
}
.journey-track { position: relative; padding: 20px 0 10px; margin: 10px 0 30px; }
.journey-line {
position: absolute; left: 27px; top: 0; bottom: 0; width: 2px;
background: linear-gradient(180deg,
var(--attractor-cyan),
var(--phase-purple) 30%,
var(--chaos-red) 60%,
var(--bifur-green) 80%,
var(--strange-gold));
opacity: 0.4;
}
.journey-node { display: flex; align-items: flex-start; gap: 18px; margin-bottom: 24px; position: relative; }
.node-dot {
width: 56px; height: 56px; border-radius: 50%;
display: flex; align-items: center; justify-content: center;
font-size: 22px; flex-shrink: 0; z-index: 2;
border: 2px solid transparent; transition: all 0.3s;
}
.node-dot:hover { transform: scale(1.1); }
.nd1 { background: rgba(0,245,255,0.15); border-color: var(--attractor-cyan); }
.nd2 { background: rgba(191,95,255,0.15); border-color: var(--phase-purple); }
.nd3 { background: rgba(255,45,85,0.15); border-color: var(--chaos-red); }
.nd4 { background: rgba(57,255,20,0.15); border-color: var(--bifur-green); }
.nd5 { background: rgba(255,215,0,0.15); border-color: var(--strange-gold); }
.node-content { padding-top: 7px; }
.node-content h3 { font-size: 1.05rem; font-weight: 700; margin-bottom: 5px; }
.node-content p { font-size: 0.8rem; color: var(--text-secondary); line-height: 1.65; }
.card, .stat-item {
animation: fadeUp 0.45s ease both;
animation-play-state: paused;
}
.card.visible, .stat-item.visible { animation-play-state: running; }
@keyframes fadeUp {
from { opacity: 0; transform: translateY(18px); }
to { opacity: 1; transform: translateY(0); }
}
::-webkit-scrollbar { width: 5px; height: 5px; }
::-webkit-scrollbar-track { background: transparent; }
::-webkit-scrollbar-thumb { background: var(--card-border); border-radius: 3px; }
::-webkit-scrollbar-thumb:hover { background: var(--phase-purple); }
footer {
position: relative; z-index: 5;
text-align: center; padding: 55px 20px;
border-top: 1px solid var(--card-border); margin-top: 50px;
}
.footer-glow {
position: absolute; bottom: 0; left: 50%; transform: translateX(-50%);
width: 500px; height: 180px;
background: radial-gradient(ellipse, rgba(191,95,255,0.07), transparent 70%);
pointer-events: none;
}
footer h3 { font-size: 1.6rem; font-weight: 800; margin-bottom: 10px; }
footer p { color: var(--text-secondary); font-size: 0.84rem; line-height: 1.8; }
/* ── BUTTERFLY EFFECT BAR ── */
.butterfly-bar {
display: flex; align-items: center; gap: 12px; flex-wrap: wrap;
padding: 10px 14px; background: rgba(255,45,85,0.06);
border: 1px solid rgba(255,45,85,0.2); border-radius: 10px;
margin-top: 10px; font-size: 11px; font-family: 'Courier New', monospace;
}
.butterfly-bar .sep-label { color: var(--text-secondary); }
.butterfly-bar .sep-val { color: var(--chaos-red); font-weight: 700; }
.butterfly-bar .lyap-live { color: var(--bifur-green); }
.butterfly-bar .lyap-live.chaotic { color: var(--chaos-red); }
</style>
</head>
<body>
<canvas id="bg-canvas"></canvas>
<!-- HEADER -->
<header>
<div class="hero-badge">🌀 Chaos Theory Masterclass 🌀</div>
<h1 class="main-title">Dynamical Systems<br>& Chaos</h1>
<p class="subtitle">
One parameter away from infinity. A butterfly flaps its wings.
The universe folds into a strange attractor and never repeats — but never escapes either.
Welcome to the mathematics of everything that moves.
</p>
<div class="nav-pills">
<button class="nav-pill np1" onclick="smoothTo('sec-foundations')">🌱 Foundations</button>
<button class="nav-pill np2" onclick="smoothTo('sec-chaos')">🌀 Routes to Chaos</button>
<button class="nav-pill np3" onclick="smoothTo('sec-bifur')">🌿 Bifurcations</button>
<button class="nav-pill np4" onclick="smoothTo('sec-attractors')">✨ Strange Attractors</button>
<button class="nav-pill np5" onclick="smoothTo('sec-advanced')">🔮 Advanced</button>
</div>
</header>
<!-- LORENZ HERO SANDBOX -->
<div class="hero-wrap">
<div class="hero-header">
<div class="hero-title-block">
<h2>🌀 Live Lorenz Attractor</h2>
<p>Drag to rotate · RK4 integration · Watch determinism become unpredictable</p>
</div>
<div class="hero-controls">
<button class="hc-btn hcb1" onclick="addTrajectory()">＋ New Trajectory</button>
<button class="hc-btn hcb2" onclick="toggleButterfly()">🦋 Butterfly Mode</button>
<button class="hc-btn hcb3" onclick="setSystem('lorenz')">Lorenz</button>
<button class="hc-btn hcb4" onclick="setSystem('rossler')">Rössler</button>
<button class="hc-btn hcb5" onclick="resetSim()">↺ Reset</button>
</div>
</div>
<div class="hero-canvas-wrap">
<canvas id="lorenzCanvas" height="500"></canvas>
<div class="hero-overlay">
<div class="ov-chip">
System: <span id="sysName">Lorenz</span><br>
Trajectories: <span id="trajCount">1</span><br>
Steps: <span id="stepCount">0</span>
</div>
<div class="ov-chip">
σ = <span id="pSigma">10.0</span><br>
ρ = <span id="pRho">28.0</span><br>
β = <span id="pBeta">2.67</span>
</div>
<div class="ov-chip" id="lyapChip" style="display:none">
λ_max ≈ <span id="lyapVal" class="lyap-pos">0.000</span><br>
sep: <span id="sepVal">1.0e-4</span><br>
<span style="font-size:9px;color:#2a1a44">divergence rate</span>
</div>
</div>
<div class="hero-sys-badge" id="sysBadge">LORENZ ATTRACTOR</div>
</div>
<div class="butterfly-bar" id="butterflyBar" style="display:none">
<span class="sep-label">🦋 Butterfly Mode:</span>
<span class="sep-label">twin trajectories, initial separation ε=1×10⁻⁴</span>
<span class="sep-label">|δx| =</span>
<span class="sep-val" id="bfSepDisplay">1.0e-4</span>
<span class="sep-label">· λ_max ≈</span>
<span class="lyap-live" id="bfLyapDisplay">—</span>
<span class="sep-label">· doubling time ≈</span>
<span class="lyap-live" id="bfDoubling">—</span>
</div>
<div class="param-panel">
<div class="param-group">
<div class="param-label">σ (SIGMA) — PRANDTL</div>
<input type="range" id="sl-sigma" min="1" max="20" step="0.1" value="10" oninput="updateParams()">
<div class="param-val" id="vl-sigma">10.0</div>
</div>
<div class="param-group">
<div class="param-label">ρ (RHO) — RAYLEIGH</div>
<input type="range" id="sl-rho" min="1" max="50" step="0.1" value="28" oninput="updateParams()">
<div class="param-val" id="vl-rho">28.0</div>
</div>
<div class="param-group">
<div class="param-label">β (BETA) — GEOMETRY</div>
<input type="range" id="sl-beta" min="0.5" max="6" step="0.05" value="2.667" oninput="updateParams()">
<div class="param-val" id="vl-beta">2.67</div>
</div>
<div class="param-group">
<div class="param-label">TRAIL LENGTH</div>
<input type="range" id="sl-trail" min="100" max="3000" step="50" value="1200" oninput="updateParams()">
<div class="param-val" id="vl-trail">1200</div>
</div>
<div class="param-group">
<div class="param-label">SPEED</div>
<input type="range" id="sl-speed" min="1" max="20" step="1" value="6" oninput="updateParams()">
<div class="param-val" id="vl-speed">6</div>
</div>
</div>
<div class="hint-bar">Drag the attractor to rotate in 3D · Slide parameters to morph the system · 🦋 Butterfly Mode shows two nearly-identical trajectories diverging exponentially</div>
</div>
<!-- MAIN CONTAINER -->
<div class="main-container">
<div class="stats-bar">
<div class="stat-item"><div class="num">∞</div><div class="lbl">Never Repeats</div></div>
<div class="stat-item"><div class="num">3</div><div class="lbl">Min Dimensions for Chaos</div></div>
<div class="stat-item"><div class="num">λ</div><div class="lbl">Lyapunov Exponent</div></div>
<div class="stat-item"><div class="num">4.669</div><div class="lbl">Feigenbaum δ</div></div>
<div class="stat-item"><div class="num">2.06</div><div class="lbl">Lorenz Dimension</div></div>
</div>
<!-- JOURNEY -->
<div class="sec-header">
<div class="sec-icon si-cyan">🗺️</div>
<div class="sec-title-grp"><h2>Your Chaos Journey</h2><p>From equilibrium to the edge of the unknowable</p></div>
</div>
<div class="journey-track">
<div class="journey-line"></div>
<div class="journey-node">
<div class="node-dot nd1">🌱</div>
<div class="node-content">
<h3 style="color:var(--attractor-cyan)">Foundations — "Systems That Evolve"</h3>
<p>ODEs, flows, fixed points, stability analysis. Phase portraits as the map of all possible behaviors. The language of dx/dt = f(x) and what it means geometrically. Linear systems solved exactly; nonlinear systems where the real adventure begins.</p>
</div>
</div>
<div class="journey-node">
<div class="node-dot nd2">🔄</div>
<div class="node-content">
<h3 style="color:var(--phase-purple)">Phase Portraits — "Geometry of Behavior"</h3>
<p>Fixed points, limit cycles, saddle points, stable/unstable manifolds. The Poincaré-Bendixson theorem. Nullclines. Every trajectory is a story; the phase portrait is the complete atlas of all possible stories for a system.</p>
</div>
</div>
<div class="journey-node">
<div class="node-dot nd3">🌀</div>
<div class="node-content">
<h3 style="color:var(--chaos-red)">Chaos — "Sensitive Dependence"</h3>
<p>Lyapunov exponents, the butterfly effect, topological mixing, dense periodic orbits. Chaos is not randomness — it's determinism so tangled it becomes unpredictable. The three ingredients: sensitivity, transitivity, density of periodics.</p>
</div>
</div>
<div class="journey-node">
<div class="node-dot nd4">🌿</div>
<div class="node-content">
<h3 style="color:var(--bifur-green)">Bifurcations — "Where Systems Change Character"</h3>
<p>Saddle-node, pitchfork, transcritical, Hopf bifurcations. The logistic map's period-doubling cascade. The Feigenbaum constant 4.669... appearing universally. Bifurcation diagrams as the autobiography of a parameter sweep.</p>
</div>
</div>
<div class="journey-node">
<div class="node-dot nd5">✨</div>
<div class="node-content">
<h3 style="color:var(--strange-gold)">Strange Attractors & Fractals — "Infinite Complexity, Finite Box"</h3>
<p>Hausdorff dimension, fractal geometry of attractors, the Lorenz butterfly, Rössler band, Chua circuit. Measure theory on sets of zero volume but nonzero information. The universe's preference for self-similar structure.</p>
</div>
</div>
</div>
<!-- ══════════════════════════════════════════ -->
<!-- SECTION 1 — FOUNDATIONS -->
<!-- ══════════════════════════════════════════ -->
<div id="sec-foundations" class="sec-header">
<div class="sec-icon si-cyan">🌱</div>
<div class="sec-title-grp">
<h2 style="color:var(--attractor-cyan)">Section 1 — Dynamical Foundations</h2>
<p>The grammar of systems that evolve in time</p>
</div>
<div class="sec-badge" style="background:rgba(0,245,255,0.08);border:1px solid var(--attractor-cyan);color:var(--attractor-cyan)">FOUNDATIONS</div>
</div>
<div class="insight-box">
<h4>The Central Object</h4>
<p>A dynamical system is simply a rule for how a state changes over time: dx/dt = f(x). That's it. From this single idea flows all of classical mechanics, population biology, economics, neuroscience, and the weather. The profound question isn't how to write the equation — it's understanding what every possible solution looks like without necessarily solving it. That's where geometry enters, and where the magic begins.</p>
</div>
<div class="key-insight">
<div class="ki-icon">💡</div>
<div class="ki-body">
<h5>Practical Insight — Why Geometry Over Algebra?</h5>
<p>Most nonlinear ODEs have no closed-form solutions — they can't be "solved" symbolically. But you can always draw the vector field and read off the qualitative behavior: fixed points, limit cycles, basins of attraction. This geometric thinking is what makes dynamical systems actually useful in science and engineering.</p>
</div>
</div>
<div class="demo-panel">
<div class="demo-tabs">
<button class="demo-tab active" onclick="switchTab(this,'phase1d')">1D Phase Line</button>
<button class="demo-tab" onclick="switchTab(this,'phase2d')">2D Phase Portrait</button>
<button class="demo-tab" onclick="switchTab(this,'nullclines')">Nullclines</button>
<button class="demo-tab" onclick="switchTab(this,'stability')">Stability</button>
</div>
<div class="demo-content active" id="tab-phase1d">
<div class="demo-2col">
<canvas id="d-phase1d" height="220"></canvas>
<div class="demo-explain">
<h4>1D Phase Line — Simplest Possible Dynamics</h4>
<p>dx/dt = f(x) in one dimension. Plot f(x) vs x — where f>0, the state moves right; where f<0, it moves left. Zeros of f are fixed points. The slope of f at a fixed point determines stability: f'(x*)<0 → stable (attracted), f'(x*)>0 → unstable (repelled).</p>
<p>This single picture contains the complete qualitative behavior of any 1D autonomous system — no integration required.</p>
<div class="code-block">
<span class="cm">// Logistic growth: dx/dt = rx(1-x)</span>
<span class="kw">f</span>(x) = r * x * (<span class="num">1</span> - x);
<span class="cm">// Fixed points: x* = 0 (unstable)</span>
<span class="cm">// x* = 1 (stable)</span>
<span class="cm">// f'(0) = r > 0 → unstable</span>
<span class="cm">// f'(1) = -r < 0 → stable ✓</span>
</div>
</div>
</div>
</div>
<div class="demo-content" id="tab-phase2d">
<div class="demo-2col">
<canvas id="d-phase2d" height="220"></canvas>
<div class="demo-explain">
<h4>2D Phase Portrait — The Full Atlas</h4>
<p>In 2D, the state is (x,y) and the velocity field is (dx/dt, dy/dt) = (f,g). Every point in the plane has an arrow showing where the system goes next. Trajectories are the integral curves of this vector field — they can never cross (uniqueness theorem).</p>
<p>Click anywhere on the canvas to drop a new trajectory and watch it evolve!</p>
<div class="code-block">
<span class="cm">// Van der Pol oscillator</span>
dx/dt = y
dy/dt = μ(<span class="num">1</span>-x²)y - x
<span class="cm">// μ=0: pure harmonic</span>
<span class="cm">// μ>0: limit cycle emerges</span>
</div>
</div>
</div>
</div>
<div class="demo-content" id="tab-nullclines">
<div class="demo-2col">
<canvas id="d-nullclines" height="220"></canvas>
<div class="demo-explain">
<h4>Nullclines — Where Motion Goes Silent in One Direction</h4>
<p>x-nullcline: the curve where dx/dt = 0 (horizontal flow). y-nullcline: where dy/dt = 0 (vertical flow). Their intersections are fixed points. The regions between nullclines have consistent direction signs — this partitions phase space into qualitative regimes without solving anything.</p>
<div class="code-block">
<span class="cm">// Predator-Prey (Lotka-Volterra)</span>
dx/dt = αx - βxy <span class="cm">// prey</span>
dy/dt = δxy - γy <span class="cm">// predator</span>
<span class="cm">// x-nullcline: x=0 or y=α/β</span>
<span class="cm">// y-nullcline: y=0 or x=γ/δ</span>
</div>
</div>
</div>
</div>
<div class="demo-content" id="tab-stability">
<div class="demo-2col">
<canvas id="d-stability" height="220"></canvas>
<div class="demo-explain">
<h4>Linear Stability — The Jacobian Tells All</h4>
<p>Linearize near a fixed point x*: δẋ = J·δx where J is the Jacobian matrix. The eigenvalues of J determine stability: both negative real parts → stable node; both positive → unstable node; opposite signs → saddle; complex with negative real part → spiral sink.</p>
<div class="code-block">
J = [∂f/∂x ∂f/∂y]
[∂g/∂x ∂g/∂y]
<span class="cm">// at fixed point: τ = tr(J), Δ = det(J)</span>
<span class="cm">// τ<0, Δ>0 → stable spiral/node</span>
<span class="cm">// Δ<0 → saddle point</span>
</div>
</div>
</div>
</div>
</div>
<div class="card-grid grid-3">
<div class="card cc">
<div class="card-glow"></div>
<div class="card-num">MODULE 1.1</div>
<div class="card-mini"><canvas id="m1c1"></canvas></div>
<h3>ODEs as Flows — Geometry Over Algebra</h3>
<p>The paradigm shift: instead of finding explicit solutions, understand the geometry of the vector field. Existence and uniqueness theorem. Autonomous vs non-autonomous systems. The flow map φₜ and what it means to compose flows.</p>
<div class="card-tags"><span class="tag">ODEs</span><span class="tag">Vector Fields</span><span class="tag">Flow Maps</span><span class="tag">Autonomous</span></div>
<div class="card-footer"><span class="duration">⏱ 75 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot"></span><span class="dot"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cc">
<div class="card-glow"></div>
<div class="card-num">MODULE 1.2</div>
<div class="card-mini"><canvas id="m1c2"></canvas></div>
<h3>Fixed Points & Their Stability</h3>
<p>Finding equilibria algebraically, classifying them geometrically. The trace-determinant plane as the complete atlas of 2D linear fixed point types. Lyapunov functions — proving stability without linearization. Basin of attraction.</p>
<div class="card-tags"><span class="tag">Fixed Points</span><span class="tag">Jacobian</span><span class="tag">Lyapunov</span><span class="tag">Basin</span></div>
<div class="card-footer"><span class="duration">⏱ 90 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cc">
<div class="card-glow"></div>
<div class="card-num">MODULE 1.3</div>
<div class="card-mini"><canvas id="m1c3"></canvas></div>
<h3>Limit Cycles — Self-Sustained Oscillation</h3>
<p>Isolated closed trajectories that attract nearby orbits. Poincaré-Bendixson theorem: chaos is impossible in 2D flows (no room to be chaotic without crossing). The Van der Pol oscillator. How biological rhythms (heartbeats, circadian clocks) are limit cycles.</p>
<div class="card-tags"><span class="tag">Limit Cycles</span><span class="tag">Van der Pol</span><span class="tag">Oscillation</span><span class="tag">P-B Theorem</span></div>
<div class="card-footer"><span class="duration">⏱ 80 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cc">
<div class="card-glow"></div>
<div class="card-num">MODULE 1.4</div>
<div class="card-mini"><canvas id="m1c4"></canvas></div>
<h3>Predator-Prey & Population Dynamics</h3>
<p>Lotka-Volterra equations — rabbits and foxes oscillating forever. Why the centers are neutrally stable (not attractors). What happens with logistic prey? The real Yellowstone data vs the model. A masterclass in what equations can and cannot capture.</p>
<div class="card-tags"><span class="tag">Lotka-Volterra</span><span class="tag">Ecology</span><span class="tag">Centers</span><span class="tag">Oscillations</span></div>
<div class="card-footer"><span class="duration">⏱ 60 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot"></span><span class="dot"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cc">
<div class="card-glow"></div>
<div class="card-num">MODULE 1.5</div>
<div class="card-mini"><canvas id="m1c5"></canvas></div>
<h3>Conservative Systems & Energy Surfaces</h3>
<p>When energy is conserved: H(x,y) = constant defines invariant curves. Hamiltonian systems, symplectic structure, Liouville's theorem (phase space volume conserved). The pendulum as the gateway between integrable and chaotic.</p>
<div class="card-tags"><span class="tag">Hamiltonian</span><span class="tag">Energy</span><span class="tag">Symplectic</span><span class="tag">Pendulum</span></div>
<div class="card-footer"><span class="duration">⏱ 90 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cc feat-card">
<div class="card-content">
<div class="card-glow"></div>
<div class="card-num">MODULE 1.6 — FEATURED</div>
<h3>The Pendulum — Every Behavior in One System</h3>
<p>Small oscillations → harmonic oscillator. Separatrix → the knife-edge between oscillation and rotation. Beyond separatrix → full rotation. A single system showing fixed points, centers, saddles, separatrices, homoclinic orbits — the complete zoo of 2D phase portrait features.</p>
<div class="card-tags">
<span class="tag">Pendulum</span><span class="tag">Separatrix</span><span class="tag">Homoclinic</span><span class="tag">Phase Portrait</span><span class="tag">Complete Zoo</span>
</div>
<div class="card-footer"><span class="duration">⏱ 2 hours</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span></div>
</div>
</div>
<canvas id="feat-pendulum"></canvas>
</div>
</div>
<div class="formula-strip">
<div class="formula-chip">ẋ = f(x,y), ẏ = g(x,y)</div>
<div class="formula-chip">J = [∂f/∂x, ∂f/∂y; ∂g/∂x, ∂g/∂y]</div>
<div class="formula-chip">τ = tr(J), Δ = det(J)</div>
<div class="formula-chip">τ² - 4Δ > 0 → nodes</div>
<div class="formula-chip">Δ < 0 → saddle</div>
<div class="formula-chip">H(x,y) = ½v² - cos(θ)</div>
<div class="formula-chip">∇·F = 0 → no limit cycles</div>
</div>
<!-- ══════════════════════════════════════════ -->
<!-- SECTION 2 — ROUTES TO CHAOS -->
<!-- ══════════════════════════════════════════ -->
<div id="sec-chaos" class="sec-header">
<div class="sec-icon si-red">🌀</div>
<div class="sec-title-grp">
<h2 style="color:var(--chaos-red)">Section 2 — Routes to Chaos</h2>
<p>Sensitive dependence, the butterfly effect, and Lyapunov's measuring stick</p>
</div>
<div class="sec-badge" style="background:rgba(255,45,85,0.08);border:1px solid var(--chaos-red);color:var(--chaos-red)">CORE CHAOS</div>
</div>
<div class="insight-box red" style="--ib-col:var(--chaos-red)">
<h4>The Butterfly Effect — Precisely Defined</h4>
<p>Edward Lorenz in 1963: a tiny rounding error in initial conditions — 0.506127 vs 0.506 — produced completely different weather simulations after two months. This is sensitive dependence on initial conditions: nearby trajectories diverge exponentially. The Lyapunov exponent λ measures this divergence rate. Chaos requires λ > 0. It's not that small causes have large effects — it's that the information required to predict the future grows without bound.</p>
</div>
<div class="key-insight red">
<div class="ki-icon">🔑</div>
<div class="ki-body">
<h5>The Real Definition of Chaos (Devaney)</h5>
<p>A dynamical system is chaotic if it has: (1) sensitive dependence on initial conditions (λ>0), (2) topological transitivity (orbits visit everywhere), and (3) dense periodic orbits (periodics are everywhere, but measure zero). Remarkably, conditions 2+3 together imply condition 1 — sensitivity is a consequence of the other two structural properties.</p>
</div>
</div>
<div class="card-grid grid-3">
<div class="card cr">
<div class="card-glow"></div>
<div class="card-num">MODULE 2.1</div>
<div class="card-mini"><canvas id="m2c1"></canvas></div>
<h3>Lyapunov Exponents — Measuring Chaos</h3>
<p>λ = lim(t→∞) (1/t) ln|δx(t)/δx(0)|. If λ>0, nearby trajectories diverge exponentially — chaos. The Lyapunov spectrum for higher-dimensional systems. The maximum Lyapunov exponent as chaos's fingerprint. How to compute λ numerically from a time series.</p>
<div class="card-tags"><span class="tag">Lyapunov</span><span class="tag">Divergence</span><span class="tag">Exponent</span><span class="tag">Measurement</span></div>
<div class="card-footer"><span class="duration">⏱ 90 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cr">
<div class="card-glow"></div>
<div class="card-num">MODULE 2.2</div>
<div class="card-mini"><canvas id="m2c2"></canvas></div>
<h3>The Logistic Map — A Universe in One Equation</h3>
<p>xₙ₊₁ = rxₙ(1−xₙ). For r<3: stable fixed point. r>3: period-2 cycle. r≈3.57: period-doubling into chaos. Beyond: windows of order amid chaos, self-similarity, universal constants. The simplest discrete map containing everything chaos theory has to say.</p>
<div class="card-tags"><span class="tag">Logistic Map</span><span class="tag">Period Doubling</span><span class="tag">Discrete</span><span class="tag">Universal</span></div>
<div class="card-footer"><span class="duration">⏱ 2 hours</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cr">
<div class="card-glow"></div>
<div class="card-num">MODULE 2.3</div>
<div class="card-mini"><canvas id="m2c3"></canvas></div>
<h3>Stretching & Folding — The Taffy Machine</h3>
<p>Chaos requires two operations: stretching (sensitivity) and folding (boundedness). The horseshoe map as the geometric prototype. Symbolic dynamics — encoding trajectories as binary sequences. How infinite complexity is generated by finite operations, repeated.</p>
<div class="card-tags"><span class="tag">Horseshoe</span><span class="tag">Symbolic Dynamics</span><span class="tag">Stretching</span><span class="tag">Folding</span></div>
<div class="card-footer"><span class="duration">⏱ 75 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cr">
<div class="card-glow"></div>
<div class="card-num">MODULE 2.4</div>
<div class="card-mini"><canvas id="m2c4"></canvas></div>
<h3>Poincaré Sections — Slicing Through Chaos</h3>
<p>Instead of a continuous trajectory, record only the state each time it pierces a chosen surface. A limit cycle becomes a fixed point. A torus becomes a closed curve. Chaos becomes a fractal cloud of points. The Poincaré map reduces continuous time to a discrete map.</p>
<div class="card-tags"><span class="tag">Poincaré Section</span><span class="tag">Return Map</span><span class="tag">Reduction</span><span class="tag">Torus</span></div>
<div class="card-footer"><span class="duration">⏱ 80 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot"></span></div>
</div>
</div>
<div class="card cr">
<div class="card-glow"></div>
<div class="card-num">MODULE 2.5</div>
<div class="card-mini"><canvas id="m2c5"></canvas></div>
<h3>The Three Routes to Chaos</h3>
<p>Period-doubling (Feigenbaum): stable cycles → 2-cycles → 4-cycles → chaos, universally. Quasiperiodicity (Ruelle-Takens): adding incommensurate frequencies fills a torus, then chaos. Intermittency (Pomeau-Manneville): long regular stretches punctuated by chaotic bursts.</p>
<div class="card-tags"><span class="tag">Period-Doubling</span><span class="tag">Quasiperiodic</span><span class="tag">Intermittency</span><span class="tag">Routes</span></div>
<div class="card-footer"><span class="duration">⏱ 90 min</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span></div>
</div>
</div>
<div class="card cr">
<div class="card-glow"></div>
<div class="card-num">MODULE 2.6</div>
<div class="card-mini"><canvas id="m2c6"></canvas></div>
<h3>Chaos vs Noise — Telling Them Apart</h3>
<p>Both look irregular. Both have power spectra with broad peaks. But chaos is deterministic: it has finite correlation dimension, positive Lyapunov exponents, and reconstructible attractors. Takens' embedding theorem: reconstruct phase space from a single time series using delay coordinates.</p>
<div class="card-tags"><span class="tag">Takens</span><span class="tag">Embedding</span><span class="tag">Delay Coords</span><span class="tag">Correlation Dim</span></div>
<div class="card-footer"><span class="duration">⏱ 2 hours</span>
<div class="diff-dots"><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span><span class="dot f"></span></div>
</div>
</div>
</div>
<!-- ══════════════════════════════════════════ -->
<!-- BIFURCATION DIAGRAM — INTERACTIVE -->
<!-- ══════════════════════════════════════════ -->
<div id="sec-bifur">
<div class="bifur-wrap">
<div class="bifur-header">
<div>
<h3>🌿 Live Bifurcation Diagram — The Logistic Map</h3>
<p>xₙ₊₁ = rxₙ(1−xₙ) · Hover to probe any r value · Watch period-doubling collapse into chaos</p>
</div>
</div>
<canvas id="bifurCanvas" height="320"></canvas>
<div class="bifur-controls">
<div class="bifur-stat" id="bifur-r">r: hover to probe</div>
<div class="bifur-stat" id="bifur-period">Period: —</div>
<div class="bifur-stat" id="bifur-feig">δ ≈ 4.669 (Feigenbaum)</div>
<div class="bifur-stat">Chaos onset: r ≈ 3.5699...</div>
</div>
</div>
</div>
<div class="insight-box green" style="--ib-col:var(--bifur-green)">
<h4>The Feigenbaum Constant — Universality's Fingerprint</h4>