Describe the matrix A you get by typing the command A = [-10:10]’*ones(1,21). Describe A’, A+i*A’, and C=C=0.1*(A+i*A’).
Type image(A+i*A’). Why does Matlab complain? Address Matlab’s complaint by entering image(abs(A+i*A’)) instead. Think about why the picture looks the way it does. (Maybe look up how the image command works.) Now type image(abs(C)). The picture isn’t that interesting. Why?
Make a matrix Z of zeros the same size as C. (Use the zeros command. It works just like the ones command we used above.) Now redefine Z by Z=Z.^2+C. (What’s with the . in Z.^2?) Do this again a bunch of times. Then do image(100*abs(Z)) and admire the low res art.
Define a matrix P=abs(Z)>5. Describe P in words. (Why is abs(Z)>5 even a matrix?) Now admire image(100*P). How are the pictures image(100*abs(Z)) and image(100*P) related? Remind yourself how these pictures represent the Mandelbrot set.
Now go back to the beginning and make higher resolution versions of all these pictures. That involves working with bigger matrices…