File:DragonCurve animation.gif
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DragonCurve_animation.gif (641 × 480 pixels, file size: 143 KB, MIME type: image/gif, looped, 29 frames, 17 s)
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[edit]DescriptionDragonCurve animation.gif |
Français : Construction de la courbe du dragon English: Dragon curve construction |
Date | |
Source | Own work |
Author | Guillaume Jacquenot |
function S = DragonCurve(pattern,MaxRecursionLevel)
% DRAGONCURVE
% This function generates a fractal curve called the dragon curve.
%
% A dragon curve is any member of a family of self-similar fractal curves,
% which can be approximated by recursive methods such as Lindenmayer
% systems.
%
% Inputs :
% - pattern : [Optional] Vector of complex that contain linear
% transformation to apply to each line segment
% - MaxRecursionLevel : [Optional] Maximum recusrion level
% Remember each time a new level is added, the
% number of line segments is doubled
% - options : [Optional] Structure with display option
%
% Outputs :
% - S : Structure that contains the line segment for each recursion level
% Just enter "plot(S(end).LineSeg,'k');" to plot the finest level
% generated
%
% See http://en.wikipedia.org/wiki/Dragon_curve
%
% 2011/07/10
% Guillaume Jacquenot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if nargin < 3
options.plot = true;
options.generateGIFAnimate = true;
options.plotConvergence = false;
if nargin < 2
MaxRecursionLevel = 15;
if nargin < 1
pattern(1) = 0.5 * (1+1i);
pattern(2) = 0.5 * (1-1i);
end
end
end
S(MaxRecursionLevel) = struct('LineSeg',[]);
npat = numel(pattern);
S(1).LineSeg = [0;pattern(1:(npat-1));1];
for level = 2:MaxRecursionLevel;
delta = diff(S(level-1).LineSeg);
S(level).LineSeg = zeros(npat^level+1,1);
S(level).LineSeg(1:npat:end) = S(level-1).LineSeg;
S(level).LineSeg(2:4:end-3) = ...
S(level-1).LineSeg(1:2:end-2) + delta(1:2:end-1) * pattern(1);
S(level).LineSeg(4:4:end-1) = ...
S(level-1).LineSeg(2:2:end-1) + delta(2:2:end ) * pattern(2);
end
if options.plot || options.generateGIFAnimate
BBox = determineBoundingBox(S);
plotDragonCurve(S,BBox);
end
if options.generateGIFAnimate
cmd = generateGIFAnimationCommand(MaxRecursionLevel);
eval(cmd);
end
if options.plotConvergence
plot_Convergence_Evolution(S);
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function plotDragonCurve(S,BBox)
figure('Color','w');
hold on
box on
axis off
MaxRecursionLevel = numel(S);
for level=1:MaxRecursionLevel
hp=plot(S(level).LineSeg,'k');
axis equal
axis(BBox);
saveas(gcf,[mfilename '_' sprintf('%03d',level)],'png');
saveas(gcf,[mfilename '_' sprintf('%03d',level)],'jpg');
plot2svg([mfilename '_' sprintf('%03d',level) '.svg']);
pause(0.5);
delete(hp);
end
plot(S(end).LineSeg,'k');
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function BBox = determineBoundingBox(S,proportionalOffset)
if nargin==1
proportionalOffset = 0.1;
end
BBox = zeros(1,4);
BBox(1) = min(real(S(end).LineSeg));
BBox(2) = max(real(S(end).LineSeg));
BBox(3) = min(imag(S(end).LineSeg));
BBox(4) = max(imag(S(end).LineSeg));
dBBoxX = BBox(2)-BBox(1);
dBBoxY = BBox(4)-BBox(3);
BBox = BBox + proportionalOffset * [-dBBoxX dBBoxX -dBBoxY dBBoxY];
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function plot_Convergence_Evolution(S)
figure
hold on
box on
title('Evolution of the length of the curve with the number of levels');
xlabel('Level');
ylabel('Log of the length');
MaxRecursionLevel = numel(S);
lengthCurve = zeros(1,MaxRecursionLevel);
for level=1:MaxRecursionLevel
lengthCurve(level) = sum(abs(diff(S(level).LineSeg)));
end
plot(log2(lengthCurve));
grid on
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function cmd = generateGIFAnimationCommand(MaxRecursionLevel)
cmd = '!convert -antialias -density 100 -delay 60 ';
for level =[1:1:MaxRecursionLevel MaxRecursionLevel-1:-1:1]
cmd = [cmd mfilename '_' sprintf('%03d',level) '.png '];
end
cmd = [cmd mfilename '.gif'];
return;
![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Matlab_Logo.png/25px-Matlab_Logo.png)
This diagram was created with MATLAB.
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:57, 10 July 2011 | ![]() | 641 × 480 (143 KB) | Gjacquenot (talk | contribs) | Reduce resolution |
20:25, 10 July 2011 | ![]() | 1,201 × 901 (401 KB) | Gjacquenot (talk | contribs) | Reduce bounding box | |
16:12, 10 July 2011 | ![]() | 1,201 × 901 (259 KB) | Gjacquenot (talk | contribs) |
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