Image:ML expansion illustration.png

Made by myself with MATLAB.

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | ‪Norsk (bokmål)‬ | ‪Norsk (nynorsk)‬ | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | ‪中文(简体)‬ | ‪中文(繁體)‬ | zh-yue-hant | +/-

[edit] Source code

function main()

%   Illustration of the Mittag-Leffler star
   
   lw=3.0;
   lightblue = [0.8 0.8 1];
   red=[0.867 0.06 0.14];
   blue = [0, 129, 205]/256;
   green = [0, 146,  70]/256;
   white=0.99*[1, 1, 1];
   
   figure(2); clf; hold on; axis equal; axis off;

%  plot central circle and its center
   O=[0, 0]; 
   radius=0.32; 
   plot_circle(O(1), O(2), radius, lw, red);
   tinyrad = 0.013;
   ball(O(1), O(2), tinyrad, red);

%  draw a spline-interpolated curve
   XX=[0.0543 -0.4058 -0.8211 -0.5463 -0.1310  0.1821  0.5847  0.2907];
   YY=[0.7796  0.3578  0.1661 -0.1597 -0.5495 -0.2748 -0.1278  0.3323];
   N=100; % how fine to make the interpolation
   [X, Y] = get_spline(N, XX, YY);
   plot(X, Y, 'LineWidth', lw, 'color', blue);

%  text
   fontsize = 26;
   tiny=0.0022*fontsize;
   text(O(1)-tiny, O(2)-tiny, '\it{a}', 'fontsize', fontsize);

%   plot a box around the figure to avoid bugs with saving to eps
   offset=0.04;
   plot(min(X)-offset, min(Y)-offset, '*', 'color', white)
   plot(max(X)+offset, max(Y)+offset, '*', 'color', white)

   saveas(gcf, 'ML_expansion_illustration.eps', 'psc2')
%  to later convert from eps to png use
   
function [xx, yy] = get_spline(N, x, y)
   
   n=length(x); 
   P=5; Q=n+2*P+1; % P will denote the amount of overlap
   
% Make the 'periodic' sequence xp=[x(1) x(2) x(3) ... x(n) x(1) x(2) x(3) ... ]
% of length Q. Same for yp.
   for i=1:Q
          j=rem(i, n)+1; % rem() is the remainder of division of i by n
          xp(i)=x(j);
          yp(i)=y(j);
   end
   
% do the spline interpolation
   t=1:length(xp);
   tt=1:(1/N):length(xp);
   xx=spline(t, xp, tt);
   yy=spline(t, yp, tt);
   
% discard the reduntant pieces
   start=N*(P-1)+1;
   stop=N*(n+P-1)+1;
   xx=xx(start:stop); 
   yy=yy(start:stop);

function plot_circle(x, y, r, lw, color)

   Theta=0:0.1:2.1*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   plot(X, Y, 'linewidth', lw, 'color', color);

function ball(x, y, r, color)
   Theta=0:0.1:2.1*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   H=fill(X, Y, color);
   set(H, 'EdgeColor', 'none');

• Mittag-Leffler star