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feat(letsplot): implement bifurcation-basic (#5119)
## Implementation: `bifurcation-basic` - letsplot Implements the **letsplot** version of `bifurcation-basic`. **File:** `plots/bifurcation-basic/implementations/letsplot.py` **Parent Issue:** #4415 --- :robot: *[impl-generate workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/23361206404)* --------- Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com> Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
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‎plots/bifurcation-basic/implementations/letsplot.py‎

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""" pyplots.ai
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bifurcation-basic: Bifurcation Diagram for Dynamical Systems
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Library: letsplot 4.9.0 | Python 3.14.3
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Quality: 93/100 | Created: 2026-03-20
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"""
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import numpy as np
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import pandas as pd
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from lets_plot import * # noqa: F403
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from lets_plot.export import ggsave as export_ggsave
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LetsPlot.setup_html() # noqa: F405
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# Data - Logistic map: x(n+1) = r * x(n) * (1 - x(n))
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# Higher resolution in chaotic regime for denser visualization
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r_stable = np.linspace(2.5, 3.45, 600)
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r_chaotic = np.linspace(3.45, 4.0, 1600)
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r_values = np.concatenate([r_stable, r_chaotic])
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transient = 250
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iterations = 100
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r_all = []
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x_all = []
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for r in r_values:
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x = 0.5
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for _ in range(transient):
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x = r * x * (1.0 - x)
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for _ in range(iterations):
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x = r * x * (1.0 - x)
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r_all.append(r)
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x_all.append(x)
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df = pd.DataFrame({"r": np.array(r_all), "x": np.array(x_all)})
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# Key bifurcation points
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bif_r = [3.0, 3.449, 3.544, 3.5699]
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segments_df = pd.DataFrame({"r": bif_r, "ymin": [0.0] * 4, "ymax": [1.0] * 4})
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# Stagger labels at different y positions to avoid overlap
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labels_df = pd.DataFrame(
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{"r": bif_r, "x": [0.93, 0.83, 0.73, 0.63], "label": ["Period-2", "Period-4", "Period-8", "Chaos"]}
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)
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# Feigenbaum point annotation
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feigen_df = pd.DataFrame({"r": [3.5699], "x": [0.05], "label": ["δ ≈ 4.669 (Feigenbaum)"]})
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# Plot with perceptually uniform viridis-based gradient
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plot = (
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ggplot(df, aes(x="r", y="x", color="r")) # noqa: F405
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+ geom_point( # noqa: F405
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size=0.4,
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alpha=0.35,
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tooltips="none",
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show_legend=False,
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sampling=sampling_pick(n=220000), # noqa: F405
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)
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+ scale_color_gradientn( # noqa: F405
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colors=["#440154", "#414487", "#2A788E", "#22A884", "#7AD151"], name="r"
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)
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+ geom_segment( # noqa: F405
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aes(x="r", y="ymin", xend="r", yend="ymax"), # noqa: F405
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data=segments_df,
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color="#AAAAAA",
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size=0.3,
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linetype="dashed",
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inherit_aes=False,
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tooltips="none",
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)
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+ geom_text( # noqa: F405
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aes(x="r", y="x", label="label"), # noqa: F405
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data=labels_df,
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size=13,
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color="#555555",
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hjust=0.5,
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vjust=0,
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inherit_aes=False,
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)
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+ geom_text( # noqa: F405
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aes(x="r", y="x", label="label"), # noqa: F405
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data=feigen_df,
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size=11,
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color="#777777",
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hjust=0,
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vjust=1,
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fontface="italic",
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nudge_x=0.02,
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inherit_aes=False,
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)
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+ guides(color="none") # noqa: F405
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+ labs( # noqa: F405
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x="Growth Rate (r)",
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y="Population (x)",
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title="bifurcation-basic · letsplot · pyplots.ai",
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caption="Logistic map: x(n+1) = r · x(n) · (1 − x(n))",
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)
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+ scale_x_continuous( # noqa: F405
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breaks=[2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0], expand=[0.02, 0], format=".2f"
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)
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+ scale_y_continuous( # noqa: F405
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breaks=[0.0, 0.2, 0.4, 0.6, 0.8, 1.0], expand=[0.02, 0], format=".1f"
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)
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+ coord_cartesian(ylim=[0, 1]) # noqa: F405
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+ ggsize(1600, 900) # noqa: F405
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+ theme_minimal() # noqa: F405
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+ theme( # noqa: F405
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axis_text=element_text(size=16, color="#555555"), # noqa: F405
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axis_title=element_text(size=20, color="#333333"), # noqa: F405
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plot_title=element_text(size=24, color="#222222", face="bold"), # noqa: F405
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plot_caption=element_text(size=13, color="#888888", face="italic"), # noqa: F405
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panel_grid_major_x=element_line(color="#E8E8E8", size=0.3), # noqa: F405
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panel_grid_major_y=element_blank(), # noqa: F405
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panel_grid_minor=element_blank(), # noqa: F405
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plot_background=element_rect(fill="#FAFAFA", color="#FAFAFA"), # noqa: F405
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panel_background=element_rect(fill="#FAFAFA", color="#FAFAFA"), # noqa: F405
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axis_ticks=element_line(color="#CCCCCC", size=0.3), # noqa: F405
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axis_line=element_line(color="#CCCCCC", size=0.4), # noqa: F405
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plot_margin=[30, 40, 20, 20],
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)
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)
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# Save
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export_ggsave(plot, filename="plot.png", path=".", scale=3)
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export_ggsave(plot, filename="plot.html", path=".")

‎plots/bifurcation-basic/metadata/letsplot.yaml‎

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library: letsplot
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specification_id: bifurcation-basic
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created: '2026-03-20T20:31:53Z'
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updated: '2026-03-20T20:57:00Z'
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generated_by: claude-opus-4-5-20251101
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workflow_run: 23361206404
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issue: 4415
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python_version: 3.14.3
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library_version: 4.9.0
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preview_url: https://storage.googleapis.com/pyplots-images/plots/bifurcation-basic/letsplot/plot.png
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preview_thumb: https://storage.googleapis.com/pyplots-images/plots/bifurcation-basic/letsplot/plot_thumb.png
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preview_html: https://storage.googleapis.com/pyplots-images/plots/bifurcation-basic/letsplot/plot.html
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quality_score: 93
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review:
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strengths:
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- Excellent density visualization with appropriate point size and alpha for 220k+
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data points
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- Strong data storytelling through color gradient, staggered bifurcation labels,
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and Feigenbaum annotation
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- Polished visual refinement with custom background, selective grid, and styled
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axis elements
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- Higher resolution sampling in chaotic regime (1600 vs 600 points) shows attention
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to data quality
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- Clean, deterministic code with appropriate use of letsplot-specific features
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weaknesses:
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- DE-01 could reach 7-8 with more distinctive typography or additional design polish
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- LM-01 could leverage more advanced letsplot grammar patterns
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image_description: 'The plot shows a bifurcation diagram of the logistic map with
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"Growth Rate (r)" on the x-axis (2.50–4.00) and "Population (x)" on the y-axis
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(0.0–1.0). Points are colored using a viridis-based gradient transitioning from
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dark purple (low r) through teal to bright green (high r). The diagram clearly
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shows the period-doubling cascade: a single stable fixed point for r < 3.0, period-2
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bifurcation at r ≈ 3.0, period-4 at r ≈ 3.449, period-8 at r ≈ 3.544, and then
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chaos. Dashed vertical gray lines mark each bifurcation point. Text labels "Period-2",
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"Period-4", "Period-8", and "Chaos" are staggered at different y positions to
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avoid overlap. An italic annotation "δ ≈ 4.669 (Feigenbaum)" appears near the
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bottom right. The title reads "bifurcation-basic · letsplot · pyplots.ai" in bold.
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A caption provides the logistic map equation. The background is a light off-white
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(#FAFAFA), with subtle vertical-only grid lines. Overall the plot is clean, professional,
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and clearly communicates the route to chaos.'
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criteria_checklist:
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visual_quality:
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score: 30
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max: 30
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items:
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- id: VQ-01
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name: Text Legibility
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score: 8
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max: 8
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passed: true
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comment: 'All font sizes explicitly set: title=24, axis_title=20, axis_text=16,
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caption=13, labels=13/11'
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- id: VQ-02
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name: No Overlap
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score: 6
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max: 6
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passed: true
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comment: Labels staggered at different y positions, no text collisions
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- id: VQ-03
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name: Element Visibility
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score: 6
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max: 6
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passed: true
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comment: Point size=0.4 with alpha=0.35 optimal for 220k-point density visualization
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- id: VQ-04
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name: Color Accessibility
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score: 4
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max: 4
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passed: true
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comment: Viridis-based gradient is colorblind-safe with excellent contrast
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- id: VQ-05
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name: Layout & Canvas
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score: 4
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max: 4
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passed: true
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comment: Plot fills canvas well with balanced margins, nothing cut off
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- id: VQ-06
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name: Axis Labels & Title
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score: 2
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max: 2
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passed: true
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comment: 'Descriptive labels with parameter notation: Growth Rate (r), Population
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(x)'
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design_excellence:
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score: 16
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max: 20
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items:
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- id: DE-01
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name: Aesthetic Sophistication
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score: 6
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max: 8
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passed: true
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comment: Custom viridis gradient, custom background, intentional typography
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hierarchy, clearly above defaults
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- id: DE-02
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name: Visual Refinement
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score: 5
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max: 6
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passed: true
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comment: Y-grid removed, subtle x-only grid, custom background, styled axis
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elements, generous margins
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- id: DE-03
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name: Data Storytelling
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score: 5
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max: 6
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passed: true
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comment: Color gradient reinforces parameter progression, staggered labels
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guide viewer, Feigenbaum annotation adds depth
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spec_compliance:
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score: 15
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max: 15
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items:
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- id: SC-01
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name: Plot Type
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score: 5
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max: 5
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passed: true
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comment: Correct bifurcation diagram
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- id: SC-02
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name: Required Features
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score: 4
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max: 4
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passed: true
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comment: 'All spec features present: small points, alpha, full cascade, labeled
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bifurcation points, transients discarded'
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- id: SC-03
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name: Data Mapping
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score: 3
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max: 3
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passed: true
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comment: X=r (parameter), Y=x (state), correct mapping
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- id: SC-04
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name: Title & Legend
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score: 3
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max: 3
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passed: true
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comment: Title format correct, no legend needed for continuous color
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data_quality:
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score: 15
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max: 15
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items:
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- id: DQ-01
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name: Feature Coverage
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score: 6
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max: 6
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passed: true
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comment: Shows stable fixed point, period-2/4/8, chaos, windows of stability,
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higher resolution in chaotic regime
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- id: DQ-02
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name: Realistic Context
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score: 5
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max: 5
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passed: true
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comment: Logistic map is canonical example with real ecology applications
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- id: DQ-03
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name: Appropriate Scale
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score: 4
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max: 4
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passed: true
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comment: Standard parameter range r=[2.5, 4.0], x=[0, 1]
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code_quality:
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score: 10
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max: 10
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items:
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- id: CQ-01
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name: KISS Structure
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score: 3
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max: 3
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passed: true
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comment: 'Clean linear flow: imports, data generation, plot, save'
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- id: CQ-02
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name: Reproducibility
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score: 2
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max: 2
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passed: true
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comment: Fully deterministic with fixed initial condition, no randomness
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- id: CQ-03
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name: Clean Imports
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score: 2
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max: 2
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passed: true
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comment: All imports used
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- id: CQ-04
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name: Code Elegance
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score: 2
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max: 2
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passed: true
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comment: Appropriate complexity, no over-engineering
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- id: CQ-05
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name: Output & API
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score: 1
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max: 1
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passed: true
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comment: Saves as plot.png via export_ggsave with scale=3
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library_mastery:
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score: 7
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max: 10
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items:
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- id: LM-01
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name: Idiomatic Usage
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score: 4
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max: 5
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passed: true
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comment: Proper ggplot grammar with aes, layered geoms, scales, themes, sampling_pick
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- id: LM-02
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name: Distinctive Features
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score: 3
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max: 5
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passed: true
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comment: Uses sampling_pick, tooltips control, export_ggsave with scale, ggsize,
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HTML export
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verdict: APPROVED
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impl_tags:
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dependencies: []
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techniques:
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- annotations
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- layer-composition
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patterns:
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- data-generation
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- iteration-over-groups
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dataprep: []
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styling:
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- custom-colormap
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- alpha-blending
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- grid-styling

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