To show cplx:

[Z,X,Y]=makegrid(-2-2*i,2+2*i,300);    
showcplx(X,Y,Z);

Showing a double root at -1, root at 0, pole at 1
Z=(Z+1).^2.*Z./(Z-1);
showcplx(X,Y,Z,0.4);

============================
For newton's method:

for k=1:10, Z=Z-(Z.^3-1)./(3*Z.^2); showcplx(X,Y,Z,0.4); R=input(''); end;
for k=1:10, Z=Z-(Z.^5-6*Z-1)./(5*Z.^4-6); showcplx(X,Y,Z,0.4); R=input(''); end;

=======================
For Mandelbrot-type Julia sets: (note use of very small adjust)

[Z,X,Y]=makegrid(-2-2*i,2+2*i,300);

This one is Cantor dust:                                 
for k=1:10, Z=Z.^2+i; showcplx(X,Y,Z,0.1); pause(0.1); end;

This is a nice connected one:
for k=1:10, Z=Z.^2+0.3*i; showcplx(X,Y,Z,0.1); pause(0.1); end;

=======================
For Mandelbrot set:
[C,X,Y]=makegrid(-2.5+1.75*i,1.0-1.75*i,300);
Z=C;
    mtx=showcplxm(X,Y,Z,0.2);
    imwrite(mtx,sprintf('mandel%d.png',1),'png');
for k=2:9, k
    Z=Z.^2+C;
    mtx=showcplxm(X,Y,Z,0.2);
    imwrite(mtx,sprintf('mandel%d.png',k),'png');
end;
for k=10:29,
  Z=Z.^2+C; k
  end;
for k=30:40, k
    Z=Z.^2+C;
    mtx=showcplxm(X,Y,Z,1.0);
    imwrite(mtx,sprintf('mandel%d.png',k),'png');
end;

 [C,X,Y]=makegrid(-2.5-1.75*i,1.0+1.75*i,300);
 Z=C;
 for k=2:40,
    Z=Z.^2+C;
showcplx(X,Y,Z,0.2); title(k); pause(0.1);
end;

mandout=double(imread('M300EDGE.png'));
mandcomp=ones(size(mandout))-mandout;
 [C,X,Y]=makegrid(-2.5+1.75*i,1.0-1.75*i,300);
 Z=C;
 for k=2:40,
    Z=Z.^2+C;
    ZD=showcplxm(X,Y,Z.*mandcomp,0.00001);
    image(ZD); title(k); pause(0.1);
end;