File:ML expansion illustration.png
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![File:ML expansion illustration.png](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/ML_expansion_illustration.png/644px-ML_expansion_illustration.png?20070416220204)
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Original file (1,621 × 1,508 pixels, file size: 77 KB, MIME type: image/png)
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Made by myself with MATLAB.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Matlab_Logo.png/25px-Matlab_Logo.png)
This diagram was created with MATLAB.
Public domainPublic domainfalsefalse |
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I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
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 redundant 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');
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This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}} .
It is recommended to name the SVG file “ML expansion illustration.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:02, 16 April 2007 | ![]() | 1,621 × 1,508 (77 KB) | Oleg Alexandrov (talk | contribs) | |
21:58, 16 April 2007 | ![]() | 1,621 × 1,508 (77 KB) | Oleg Alexandrov (talk | contribs) | ||
05:29, 14 April 2007 | ![]() | 1,081 × 1,006 (40 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD-self}} | |
05:28, 14 April 2007 | ![]() | 1,081 × 1,006 (40 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD-self}} | |
05:27, 14 April 2007 | ![]() | 1,351 × 1,257 (52 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD-self}} | |
05:23, 14 April 2007 | ![]() | 1,081 × 1,006 (40 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD-self}} |
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