I am trying to generate code for plotting anti fractals and getting error

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.

[Walter Roberson]

I cannot find any Mathworks or File Exchange function named Q_c ?

It would be easier if you posted your code, and also posted the error messages you are encountering.

[Akansha]

i need this output. i am not getting correct output by this code and Q_c{z)=z^2+c

%Constants

dr = 800;                       % Increased resolution of the grid
xmin = -6; xmax = 4.7;          % Real range
ymin = -5.5; ymax = 5.5;        % Imaginary range
K = 200;                        % Increased maximum number of iterations
theta = 0.2;                    % Parameter theta
k = 2;                          % Parameter k
M = 256;                        % Number of colors in the colormap

% 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 = 0;                  % Initial z0
        n = 0;                  % Iteration counter

        % Iterate using the Tricorn function
        while n <= K
            u_n = (1 - theta) * z + theta * (conj(z)^2 + c);  % Compute u_n
            z_next = conj(u_n)^2 + 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) = floor((M - 1) * n / K);  % Store escape time
    end
end

% Plotting the fractal
figure; % Create a new figure
imagesc(re, im, E); % Display the escape time matrix
colormap(jet(M)); % 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

[Walter Roberson]

Your code does not include any Q_c function, so it is difficult to figure out what you are talking about.

[Akansha]

my function Qc(z)=conj(z)^2+c , which is defined by u_n = (1 - theta) * z + theta * (conj(z)^2 + c); this part of my code

[KSSV]

Copy your full code here....Show us how did you run along with the input.

[Walter Roberson]

? It looks more like

z_next = conj(u_n)^2 + c;

matches to your Qc(z) definition ?

[Akansha]

[Akansha]

this is the whole algorithm i am trying to generate code for this algorithm but not getting the correct output

[Akansha]

[Akansha]

this output i need but not getting

Answer 1

[Voss]

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).