% Compute the image of a rectangular grid under a a conformal map.  function main()     N = 15; % num of grid points    epsilon = 0.1; % displacement for each small diffeomorphism    num_comp = 10; % number of times the diffeomorphism is composed with itself      S = linspace(-1, 1, N);     [X, Y] = meshgrid(S);         % graphing settings    lw = 1.0;     % KSmrq's colors    red    = [0.867 0.06 0.14];    blue   = [0, 129, 205]/256;    green  = [0, 200,  70]/256;    yellow = [254, 194,   0]/256;    white = 0.99*[1, 1, 1];     mycolor = blue;        % start plotting    figno=1; figure(figno); clf;     shiftx = 0; shifty = 0; scale = 1;    do_plot(X, Y, lw, figno, mycolor, shiftx, shifty, scale)     I=sqrt(-1);    Z = X+I*Y;     % tweak these numbers for a pretty map    z0 = 1+ 2*I;    z1 = 0.1+ 0.2*I;    z2 = 0.2+ 0.3*I;    a = 0.01;    b = 0.02;    shiftx = 0.1; shifty = 1.2; scale = 1.4;    F = (Z+z0).^2 +a*(Z+z1).^3 +b*(Z+z2).^4;    F = (1+2*I)*F;        XF = real(F); YF=imag(F);     do_plot(XF, YF, lw, figno, mycolor, shiftx, shifty, scale)     axis ([-1 1.3 -2 2]); axis off;     saveas(gcf, 'Conformal_map.eps', 'psc2');         function do_plot(X, Y, lw, figno, mycolor, shiftx, shifty, scale)    figure(figno); hold on;     [M, N] = size(X);     X = X - min(min(X));    Y = Y - min(min(Y));     a = max(max(max(abs(X))), max(max(abs(Y))));    X = X/a; Y = Y/a;     X = scale*(X-shiftx);    Y = scale*(Y-shifty);        for i=1:N       plot(X(:, i), Y(:, i), 'linewidth', lw, 'color', mycolor);       plot(X(i, :), Y(i, :), 'linewidth', lw, 'color', mycolor);    end %   axis([-1-small, 1+small, -1-small, 1+small]);    axis equal; axis off;