fix the linting (pass ci); remove the redundant style;

Author: youssefadly237

content/about.md

@@ -7,5 +7,4 @@ showDate = false
 
 {{< img src="/Me.png" width="30" >}}
 
-
 I'm Mina. I'm a student of pure mathematics and an artist who expresses mathematical structures through visual means. My work lies somewhere between rigorous thinking and creative expression. I find my ideas in combinatorics, number patterns (I have done some research on Fibonacci and related visual proofs), and geometric shapes that appear in analysis and algebra. I find pleasure in expressing a theorem, recursion, or matrix as a composition that emphasizes symmetry, tension, and surprise.

content/posts/Random-Horse(Paths).md

@@ -10,7 +10,6 @@ tags = ['Random', 'Recursion']
 # ]
 +++
 
-
 For each index $m\in{0,\dots,20}$ define a discrete planar random walk $f_m:{0,1,\dots,1000}\to\mathbb{Z}^2$ by the recurrence
 
 $$
@@ -53,29 +52,27 @@ which looks like the following [graph](#fig-1).
 
     \draw[thin,->] (-2.2,0) -- (2.2,0) node[right] {$x$};
     \draw[thin,->] (0,-2.2) -- (0,2.2) node[above] {$y$};
+
 \end{tikzpicture}
 {{< /tikz >}}
 Graphing all possible branches of $f_{k-1} \to f_k \to f_{k+1}$, we notice that exactly one of the four possible steps from $f_k$ leads back to $f_{k-1}$, giving a probability of $\frac{1}{4}$ of returning, which explains the isolated spikes observed in the [graph](#fig-2).
 {{< tikz >}}
 \begin{tikzpicture}[>=stealth,thick, transform shape, scale=2]
 
 \tikzset{
-  n0/.style={circle,fill=orange!80!red,   inner sep=4pt},
-  n1/.style={circle,fill=blue!60!black,   inner sep=3pt},
-  n2/.style={circle,fill=teal!60!black,   inner sep=2pt},
-  a0/.style={->,orange!80!red,  thick, shorten >=3pt, shorten <=3pt},
-  a1/.style={->,blue!60!black,  thick, shorten >=3pt, shorten <=3pt},
-  ab/.style={->,teal!60!black,  thick, shorten >=7pt, shorten <=3pt},
+n0/.style={circle,fill=orange!80!red, inner sep=4pt},
+n1/.style={circle,fill=blue!60!black, inner sep=3pt},
+n2/.style={circle,fill=teal!60!black, inner sep=2pt},
+a0/.style={->,orange!80!red, thick, shorten >=3pt, shorten <=3pt},
+a1/.style={->,blue!60!black, thick, shorten >=3pt, shorten <=3pt},
+ab/.style={->,teal!60!black, thick, shorten >=7pt, shorten <=3pt},
 }
 
-
 \draw[teal!60!black, line width=1.6pt] (0,0) circle (9pt);
 
-
-\node[n0] (r)  at (0,0)   {};
+\node[n0] (r) at (0,0) {};
 \node[font=\scriptsize, orange!70!black] at (0,0.75) {$f_{k-1}$};
 
-
 \node[n1] (k1) at ( 2.2, 2.2) {};
 \node[n1] (k2) at ( 2.2,-2.2) {};
 \node[n1] (k3) at (-2.2, 2.2) {};
@@ -89,7 +86,6 @@ Graphing all possible branches of $f_{k-1} \to f_k \to f_{k+1}$, we notice that
 \draw[a0](r)--(k1); \draw[a0](r)--(k2);
 \draw[a0](r)--(k3); \draw[a0](r)--(k4);
 
-
 \node[n2] at ( 4.4, 4.4) {};
 \node[n2] at ( 4.4, 0.0) {};
 \node[n2] at ( 0.0, 4.4) {};
@@ -105,15 +101,13 @@ Graphing all possible branches of $f_{k-1} \to f_k \to f_{k+1}$, we notice that
 \draw[a1](k2)--( 0.0,-4.4);
 \draw[ab](k2)--(r);
 
-
 \node[n2] at (-4.4, 4.4) {};
 \node[n2] at (-4.4, 0.0) {};
 \draw[a1](k3)--( 0.0, 4.4);
 \draw[a1](k3)--(-4.4, 4.4);
 \draw[a1](k3)--(-4.4, 0.0);
 \draw[ab](k3)--(r);
 
-
 \node[n2] at (-4.4,-4.4) {};
 \draw[a1](k4)--( 0.0,-4.4);
 \draw[a1](k4)--(-4.4, 0.0);
@@ -122,14 +116,14 @@ Graphing all possible branches of $f_{k-1} \to f_k \to f_{k+1}$, we notice that
 
 % legend
 \draw[teal!60!black,line width=1.4pt] (5.8, 0.6) circle (5.5pt);
-\fill[orange!80!red]  (5.8, 0.6) circle (3.5pt);
-\fill[blue!60!black]  (5.8, 0.0) circle (2.8pt);
-\fill[teal!60!black]  (5.8,-0.6) circle (2.0pt);
+\fill[orange!80!red] (5.8, 0.6) circle (3.5pt);
+\fill[blue!60!black] (5.8, 0.0) circle (2.8pt);
+\fill[teal!60!black] (5.8,-0.6) circle (2.0pt);
 \node[font=\scriptsize,orange!70!black] at (7.2, 0.6) {$f_{k-1}$};
-\node[font=\scriptsize,blue!60!black]   at (7.2, 0.0) {$f_{k}$};
-\node[font=\scriptsize,teal!60!black]   at (7.2,-0.6) {$f_{k+1}$};
+\node[font=\scriptsize,blue!60!black] at (7.2, 0.0) {$f_{k}$};
+\node[font=\scriptsize,teal!60!black] at (7.2,-0.6) {$f_{k+1}$};
 \draw[ab,shorten >=0pt,shorten <=0pt]
-  (6.6,-1.2)--(5.6,-1.2);
+(6.6,-1.2)--(5.6,-1.2);
 \node[font=\scriptsize,teal!60!black] at (6.5,-1.5) {returns to $f_{k-1}$};
 
 \end{tikzpicture}
@@ -141,29 +135,29 @@ where $f_{k+4} = f_k$, yet $f_k \neq f_{k+2}$ and $f_{k+1} \neq f_{k+3}$, tracin
 \begin{tikzpicture}[>=stealth,thick, transform shape, scale=2]
 
 \tikzset{
-  pt/.style={circle, fill, inner sep=3.5pt},
-  arr/.style={->, thick, shorten >=4pt, shorten <=4pt},
+pt/.style={circle, fill, inner sep=3.5pt},
+arr/.style={->, thick, shorten >=4pt, shorten <=4pt},
 }
 
 % dashed diamond outline
 \draw[dashed, gray!45, thin]
-  (0,0) -- (2,2) -- (4,0) -- (2,-2) -- cycle;
+(0,0) -- (2,2) -- (4,0) -- (2,-2) -- cycle;
 
 % step labels along each edge
-\node[font=\tiny, gray] at (0.6,  1.4) {$(+1,+1)$};
-\node[font=\tiny, gray] at (3.4,  1.4) {$(+1,-1)$};
+\node[font=\tiny, gray] at (0.6, 1.4) {$(+1,+1)$};
+\node[font=\tiny, gray] at (3.4, 1.4) {$(+1,-1)$};
 \node[font=\tiny, gray] at (3.4, -1.4) {$(-1,-1)$};
 \node[font=\tiny, gray] at (0.6, -1.4) {$(-1,+1)$};
 
 % arrows
 \draw[->, thick, blue!70!black, shorten >=4pt, shorten <=4pt]
-  (0,0) -- (2,2);
+(0,0) -- (2,2);
 \draw[->, thick, blue!70!black, shorten >=4pt, shorten <=4pt]
-  (2,2) -- (4,0);
+(2,2) -- (4,0);
 \draw[->, thick, blue!70!black, shorten >=4pt, shorten <=4pt]
-  (4,0) -- (2,-2);
+(4,0) -- (2,-2);
 \draw[->, line width=1.8pt, teal!60!black, shorten >=7pt, shorten <=4pt]
-  (2,-2) -- (0,0);
+(2,-2) -- (0,0);
 
 % teal ring on f_k to show loop closure
 \draw[teal!60!black, line width=1.8pt] (0,0) circle (7pt);
@@ -175,15 +169,15 @@ where $f_{k+4} = f_k$, yet $f_k \neq f_{k+2}$ and $f_{k+1} \neq f_{k+3}$, tracin
 \fill[blue!60!black] (2,-2) circle (3.0pt);
 
 % labels
-\node[font=\scriptsize, orange!70!black] at (-0.75,  0.25) {$f_k$};
-\node[font=\scriptsize, teal!60!black]   at (-0.75, -0.35) {$=f_{k+4}$};
-\node[font=\scriptsize, blue!60!black]   at ( 2.0,   2.6)  {$f_{k+1}$};
-\node[font=\scriptsize, blue!60!black]   at ( 4.75,  0.0)  {$f_{k+2}$};
-\node[font=\scriptsize, blue!60!black]   at ( 2.0,  -2.6)  {$f_{k+3}$};
+\node[font=\scriptsize, orange!70!black] at (-0.75, 0.25) {$f_k$};
+\node[font=\scriptsize, teal!60!black] at (-0.75, -0.35) {$=f_{k+4}$};
+\node[font=\scriptsize, blue!60!black] at ( 2.0, 2.6) {$f_{k+1}$};
+\node[font=\scriptsize, blue!60!black] at ( 4.75, 0.0) {$f_{k+2}$};
+\node[font=\scriptsize, blue!60!black] at ( 2.0, -2.6) {$f_{k+3}$};
 
 % caption
 \node[font=\scriptsize] at (2.0, -3.6)
-  {4 diagonal steps close a square: $f_{k+4}=f_k$};
+{4 diagonal steps close a square: $f_{k+4}=f_k$};
 
 \end{tikzpicture}
 {{< /tikz >}}

static/images/horserandom.svg

@@ -6,9 +6,3 @@
 </title>
 <link rel="icon" type="image/svg+xml" href="{{ site.Home.RelPermalink }}favicon.svg" />
 {{ partialCached "head/css.html" . }} {{ partialCached "head/js.html" . }}
-<style>
-  /* tikzjax SVG text uses the loaded fonts.css classes */
-  .tikzjax svg text {
-    font-family: "Computer Modern", serif;
-  }
-</style>