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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"><html xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <!--This HTML is auto-generated from an M-file.To make changes, update the M-file and republish this document. --> <title>DRAGON CURVE (aka JURASSIC PARK FRACTAL)</title> <meta name="generator" content="MATLAB 7.3"> <meta name="date" content="2007-01-09"> <meta name="m-file" content="dragon_curve"><style>body { background-color: white; margin:10px;}h1 { color: #990000; font-size: x-large;}h2 { color: #990000; font-size: medium;}/* Make the text shrink to fit narrow windows, but not stretch too far in wide windows. */ p,h1,h2,div.content div { max-width: 600px; /* Hack for IE6 */ width: auto !important; width: 600px;}pre.codeinput { background: #EEEEEE; padding: 10px;}@media print { pre.codeinput {word-wrap:break-word; width:100%;}} span.keyword {color: #0000FF}span.comment {color: #228B22}span.string {color: #A020F0}span.untermstring {color: #B20000}span.syscmd {color: #B28C00}pre.codeoutput { color: #666666; padding: 10px;}pre.error { color: red;}p.footer { text-align: right; font-size: xx-small; font-weight: lighter; font-style: italic; color: gray;} </style></head> <body> <div class="content"> <h1>DRAGON CURVE (aka JURASSIC PARK FRACTAL)</h1> <introduction> <p>The Dragon Curve is a fractal that was made famous in <b>Jurassic Park</b>, a novel by Michael Crichton. </p> <p>This file calculates and plots the Dragon Curve. The user is encouraged to make their own variations of the fractal by experimenting with the following options: </p> <div> <ul> <li>Initial starting shape</li> <li>Angle of rotation</li> <li>Number of fractal iterations</li> </ul> </div> <p>NOTE: In order to prevent users from exceeding the memory capacities of their machines, there is a <tt>MAX_LENGTH</tt> variable that will limit the number of fractal iterations calculated. On my machine, setting this value greater than <tt>5e6</tt> becomes very taxing for the <tt>plot</tt> function, but the user is free to change it if they have more memory resources available. </p> <p>DISCLAIMER: This script can be a bit addicting! So enjoy being creative, but please be careful to keep one eye on the clock! :c) </p> <p>AUTHOR: Joseph Kirk (c) 5/2006 EMAIL: jdkirk630 at gmail dot com</p> </introduction> <h2>Contents</h2> <div> <ul> <li><a href="#1">DEFINE THE INITIAL SHAPE</a></li> <li><a href="#2">SPECIFY THE ROTATING ANGLE (DEGREES)</a></li> <li><a href="#3">SPECIFY THE NUMBER OF DESIRED FRACTAL ITERATIONS</a></li> <li><a href="#4">LIMIT THE SIZE OF THE FRACTAL</a></li> <li><a href="#5">GENERATE THE FRACTAL</a></li> <li><a href="#6">PLOT THE X,Y COORDINATES</a></li> </ul> </div> <h2>DEFINE THE INITIAL SHAPE<a name="1"></a></h2> <p>The traditional Dragon Curve uses a straight line as the initial shape, but any starting shape will work! Below is a list of some of my favorites: </p> <div> <ul> <li><tt>x=[0 1]; y=[0 0]; %LINE</tt></li> <li><tt>x=linspace(0,2*pi,50); y=-1.5*sin(x); %S-CURVE</tt></li> <li><tt>x=[0 1/3 0 1/3 0]; y=[0 1/4 1/2 3/4 1]; %W-CURVE</tt></li> <li><tt>t=linspace(0,2*pi/3,20); x=sin(t); y=cos(t); %ARC</tt></li> </ul> </div><pre class="codeinput"><span class="comment">% The x and y vectors must have at least two points each (or the result</span><span class="comment">% will just be a single point) and they must have the same length</span>x=[1 0]; y=[0 0]; <span class="comment">%LINE</span></pre><h2>SPECIFY THE ROTATING ANGLE (DEGREES)<a name="2"></a></h2> <p>The traditional Dragon Curve uses a rotating angle of 90 degrees, but any angle can be specified here. The most interesting fractals seem to be generated using angles between 80 and 120 </p><pre class="codeinput">angle=90; <span class="comment">%degrees</span></pre><h2>SPECIFY THE NUMBER OF DESIRED FRACTAL ITERATIONS<a name="3"></a></h2> <p>Good choices for this number are generally between 5 and 20, depending on the length of the starting shape and the desired resolution. </p><pre class="codeinput">n=13;</pre><h2>LIMIT THE SIZE OF THE FRACTAL<a name="4"></a></h2> <p>This is to prevent users from using too much memory.</p><pre class="codeinput">MAX_LENGTH=5e6;</pre><h2>GENERATE THE FRACTAL<a name="5"></a></h2><pre class="codeinput"><span class="comment">% Verify that we have valid (x,y) pairs</span><span class="keyword">if</span> length(x)~=length(y) disp(<span class="string">'ERROR: x and y vectors must have the same length'</span>); <span class="keyword">return</span><span class="keyword">end</span><span class="comment">% Limit the size of the fractal</span>m=length(x);<span class="keyword">if</span> ((m-1)*2^(n-1)+1) > MAX_LENGTH n=ceil(log2((MAX_LENGTH-1)/(m-1))); disp([<span class="string">'WARNING: maximum iterations exceeded ... setting n = '</span> num2str(n)]);<span class="keyword">end</span><span class="comment">% Generate the fractal</span><span class="keyword">for</span> k=1:n-1 xr = fliplr(x); yr = fliplr(y); a = x(length(x)); b = y(length(y)); [theta, rho]=cart2pol(xr - a,yr - b); [rx0, ry0] = pol2cart(theta + angle*pi/180, rho); rx = rx0 + a; ry = ry0 + b; x=[x rx(2:length(rx))]; y=[y ry(2:length(rx))];<span class="keyword">end</span></pre><h2>PLOT THE X,Y COORDINATES<a name="6"></a></h2><pre class="codeinput">figure;plot(x,y,<span class="string">'k'</span>);axis <span class="string">equal</span>axis <span class="string">off</span>title([<span class="string">'Dragon Curve (n = '</span> num2str(n) <span class="string">', angle = '</span> num2str(angle) <span class="string">')'</span>]);set(gcf,<span class="string">'color'</span>,<span class="string">'white'</span>);</pre><img vspace="5" hspace="5" src="dragon_curve_01.png"> <p class="footer"><br> Published with MATLAB® 7.3<br></p> </div> <!--##### SOURCE BEGIN #####%% DRAGON CURVE (aka JURASSIC PARK FRACTAL)
% The Dragon Curve is a fractal that was made famous in *Jurassic Park*, a
% novel by Michael Crichton.
%
% This file calculates and plots the Dragon Curve. The user is encouraged
% to make their own variations of the fractal by experimenting with the
% following options:
%
% * Initial starting shape
% * Angle of rotation
% * Number of fractal iterations
%
% NOTE: In order to prevent users from exceeding the memory capacities of
% their machines, there is a |MAX_LENGTH| variable that will limit the
% number of fractal iterations calculated. On my machine, setting this
% value greater than |5e6| becomes very taxing for the |plot| function, but
% the user is free to change it if they have more memory resources
% available.
%
% DISCLAIMER: This script can be a bit addicting! So enjoy being creative,
% but please be careful to keep one eye on the clock! :c)
%
% AUTHOR: Joseph Kirk (c) 5/2006
% EMAIL: jdkirk630 at gmail dot com
%% DEFINE THE INITIAL SHAPE
% The traditional Dragon Curve uses a straight line as the initial shape,
% but any starting shape will work! Below is a list of some of my favorites:
%
% * |x=[0 1]; y=[0 0]; %LINE|
% * |x=linspace(0,2*pi,50); y=-1.5*sin(x); %S-CURVE|
% * |x=[0 1/3 0 1/3 0]; y=[0 1/4 1/2 3/4 1]; %W-CURVE|
% * |t=linspace(0,2*pi/3,20); x=sin(t); y=cos(t); %ARC|
%
% The x and y vectors must have at least two points each (or the result
% will just be a single point) and they must have the same length
x=[1 0]; y=[0 0]; %LINE
%% SPECIFY THE ROTATING ANGLE (DEGREES)
% The traditional Dragon Curve uses a rotating angle of 90 degrees, but any
% angle can be specified here. The most interesting fractals seem to be
% generated using angles between 80 and 120
angle=90; %degrees
%% SPECIFY THE NUMBER OF DESIRED FRACTAL ITERATIONS
% Good choices for this number are generally between 5 and 20, depending on
% the length of the starting shape and the desired resolution.
n=13;
%% LIMIT THE SIZE OF THE FRACTAL
% This is to prevent users from using too much memory.
MAX_LENGTH=5e6;
%% GENERATE THE FRACTAL
% Verify that we have valid (x,y) pairs
if length(x)~=length(y)
disp('ERROR: x and y vectors must have the same length');
return
end
% Limit the size of the fractal
m=length(x);
if ((m-1)*2^(n-1)+1) > MAX_LENGTH
n=ceil(log2((MAX_LENGTH-1)/(m-1)));
disp(['WARNING: maximum iterations exceeded ... setting n = ' num2str(n)]);
end
% Generate the fractal
for k=1:n-1
xr = fliplr(x); yr = fliplr(y); a = x(length(x)); b = y(length(y));
[theta, rho]=cart2pol(xr - a,yr - b);
[rx0, ry0] = pol2cart(theta + angle*pi/180, rho);
rx = rx0 + a; ry = ry0 + b;
x=[x rx(2:length(rx))];
y=[y ry(2:length(rx))];
end
%% PLOT THE X,Y COORDINATES
figure;plot(x,y,'k');
axis equal
axis off
title(['Dragon Curve (n = ' num2str(n) ', angle = ' num2str(angle) ')']);
set(gcf,'color','white');
##### SOURCE END #####--> </body></html>⌨️ 快捷键说明
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