I am trying to generate code for plotting anti fractals and getting error
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i am taling k=2 in this function Q_c(z) ,thetha=0.2 ,A = [−6, 4.7] × [−5.5, 5.5] tri-corn generated in PMO .i am getting error in my code.
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Accepted Answer
Voss
on 30 Oct 2024
Picking z0=c instead of z0=0, correcting the definition of R_base to have 2/theta instead of 2*theta, decreasing the max number of iterations so you can see some color variation, and choosing a similar colormap, gets you closer to the reference image:
%Constants
cmap = [234 55 36; 234 84 40; 238 124 50; 243 178 62; 244 193 67; 246 235 78; 221 250 82; 112 238 113; 40 59 126; 0 0 0]/255;
M = size(cmap,1); % Number of colors in the colormap
dr = 800; % Increased resolution of the grid
xmin = -6; xmax = 4.7; % Real range
ymin = -5.5; ymax = 5.5; % Imaginary range
K = M-1; % maximum number of iterations
theta = 0.2; % Parameter theta
k = 2; % Parameter k
% Create a grid of complex numbers over A
re = linspace(xmin, xmax, dr); % Real part
im = linspace(ymin, ymax, dr); % Imaginary part
c_grid = re + im.' * 1i; % Complex grid A = [-6, 4.7] x [-5.5, 5.5]
% Initialize escape time matrix
E = zeros(size(c_grid)); % Escape time matrix
% Pre-calculate fixed R based on theta and k
R_base = (2 / theta)^(1 / (k - 1));
% Loop over each point in the grid A
for a = 1:dr
for b = 1:dr
c = c_grid(a, b); % Current point in A
R = max(abs(c), R_base); % Calculate R for this c
z = c; % Initial z0
n = 0; % Iteration counter
% Iterate using the Tricorn function
while n <= K
u_n = (1 - theta) * z + theta * (conj(z)^k + c); % Compute u_n
z_next = conj(u_n)^k + c; % Compute z_{n+1}
% Check for escape condition
if abs(z_next) > R
break;
end
z = z_next; % Update z
n = n + 1; % Increment iteration counter
end
% Map n to a color index
E(a, b) = n;
end
end
% Plotting the fractal
figure; % Create a new figure
imagesc(re, im, E); % Display the escape time matrix
colormap(cmap); % Use 'jet' colormap (replace with 'parula', 'hot', etc. if desired)
axis xy; % Correct the axis orientation
set(gca, 'YDir', 'normal'); % Ensure imaginary axis direction is correct
colorbar; % Add a colorbar
title('Anti-Fractal (Tricorn) with PMO Method');
xlabel('Real axis');
ylabel('Imaginary axis');
axis([xmin xmax ymin ymax]); % Set axis limits explicitly
The pseudo-code snippet you posted (Algorithm 2) is for Anti-Julia set, but the reference image you posted is a tricorn, which is based on Algorithm 1, as defined in the attached pdf (downloaded from here).
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