% complex_plot generates surface and contour plots of the magnitude
%  (or modulus) of a function of a complex variable z = x + i*y.

% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
%
% Revision history:
%   18-Apr-2005 -- original version for Physics 263
%

clear;    % this sets variables to zero, so we start with a clean slate

xmin = -2;  xmax = 2;   % set the minimum and maximum values of x
ymin = -2;  ymax = 2;   % set the minimum and maximum values of y
num_pts = 50;           % set the number of points in each direction

% Set a grid X Y with evenly spaced points
[X Y] = meshgrid( linspace(xmin,xmax,num_pts), linspace(ymin,ymax,num_pts) );

% Define z = x + i*y for each point in the grid
Z = X + i*Y;

% Here is where we evaluate the function we want to study.
%  Note the use of "." before operations like "^" and "/".
f = abs( Z ./ (1 + Z.^2) );    % use "abs" to take the modulus of the function

figure(1);                   % figure 1 will be a surface plot
surf(X,Y,f); colorbar;       % make the plot and add a color bar
xlabel('x-axis');  ylabel('y-axis');   % add labels to x and y axes

figure(2);                               % figure 2 will be a contour plot 
num_contours = 10;                       % use num_contours contour lines
contourf(X,Y,f,num_contours); colorbar;  % make the plot and add a color bar
xlabel('x-axis');  ylabel('y-axis');     % add labels