Complex plain transformation, task 3 N = 8

matan.m

function [ output_args ] = untitled2( input_args )
figure 
hold on

n = 8; % too lazy to hold shift

center = (2*n+1 - 1i*n) / (n+5);
radius = (n+3)/(2*n+1);
% plot(real(center), imag(center), '.g')

fromZ = @(z) abs(z-center);

veryBigNumber = 10;

fromG = zeros(veryBigNumber, veryBigNumber);
toG   = zeros(veryBigNumber, veryBigNumber);
% for x = -3:0.05:3
% % for x = real(center)-radius-0.2:0.05:real(center)+radius+0.2
%     for y = -3:0.05:3
% %     for y = imag(center)-radius-0.2:0.05:imag(center)+radius+0.2
%         z = x + 1i*y;
% %         abs(fromZ(z) - radius)
%         if (fromZ(z) > radius)
%             plot(x, y, '*r')
% %             fromG(x+veryBigNumber+1,y+veryBigNumber+1) = 1;
%             newZ = transform(z, radius, center, n);
% %             if (abs(real(newZ)) > 10 || abs(imag(newZ)) > 10) 
% %                continue 
% %             end
%             plot(real(newZ), imag(newZ), '*g')
%         else
%         end
%     end
% end

for fi = 0:0.01:2*pi
   z = center + radius*exp(1i*fi);
   newZ = transform(z, radius, center, n);
   
%    plot(real(z), imag(z), '*r')
   plot(real(newZ), imag(newZ), '*g')
   
   xlim([-0.3 3])
   ylim([-6 1])
end

end

function [newZ] = transform(z, radius, center, n)
    % Move to (0,0)
    w(1) = z - center;
    
    % Transform to identity circle
    w(2) = w(1) * 1.0/radius;
    
    % Inverse
    w(3) = 1/w(2);
    
    % Make plane
    w(4) = 1i*(w(3)+1)/(1-w(3));
    
    % Create angle
    angle = (-1)^n * (4*pi) / (5*n+3) - (-1)^(n+1)*(pi*(2*n+4)/(5*n+3));
    w(5) = w(4)^(24/43);
    
    % Rotate
    w(6) = w(5)*exp(-1i*20*pi/43);
%     w(6) = w(5)*exp(-1i*pi/2);
    
    % Move
    w(7) = w(6)-(n*1i+n+1)/(2*n-1i*n);
    
    newZ = w(end);
end