Julia set: maps with complex numbers
The Julia set is the points on the complex plane that remain bounded under iteration of the map for some complex number
.
This code is adapted from the book "MATLAB Guide" by Desmond J. Higham and Nicholas J. Higham (the constant c and the region used to generate the region are more customized).
The examples are take from the book A first course in chaotic dynamical systems by Robert L. Devalney.
Julia Set "Dragon" with ![](data:image/png;base64,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)
x = linspace(-1.3,1.3,501);
y = linspace(-1.3,1.3,501);
[X,Y] = meshgrid(x,y);
c = 0.360284+0.100376*1i;
C = ones(size(X))*c;
Z_max = 1e6; it_max = 50;
Z = complex(X,Y);
B = zeros(size(C));
for k = 1:it_max
Z = Z.^2 + C;
B = B + (abs(Z)<2);
end
% only show those bounded points
imagesc(B);
colormap(jet);
title('Julia Set "Dragon" for $c=0.360284+0.100376i$','FontSize',16,'interpreter','latex');
axis off
Julia Set with ![](data:image/png;base64,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)
x = linspace(-1.6,1.6,501);
y = linspace(-1.3,1.3,501);
[X,Y] = meshgrid(x,y);
c = -0.75+0.1i;
C = ones(size(X))*c;
Z_max = 1e6; it_max = 50;
Z = complex(X,Y);
B = zeros(size(C));
for k = 1:it_max
Z = Z.^2 + C;
B = B + (abs(Z)<0.6);
end
imagesc(B);
colormap(jet);
title('Julia Set for $c=-0.75+0.1i$','FontSize',16,'interpreter','latex');
axis off