dragon_curve.m

以matlab畫碎形中的dragon curve

%% 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');