The following is a solution set for a function f(z) =z^4+8iz^2-25. The roots of the function are

2-i, -2+i, -1+2i and 1-2i

The color shows which values will converge to the solution in the complex place

The complete matlab program is as below

% Using Newton Basin method to plot in complex plane

% The complex function is z^4+8iz^2-25

% There are 4 roots 2-i, -2+i, -1+2i and 1-2i of the above function

% It shows how starting with different points root converge

tol =.01;

a=0;

b=2;

c=0;

d=2;

m=1000;

n=1000;

x=linspace(a,b,m); % Setting up the x axis Coordinate System a to b

y=linspace(c,d,n); % Setting up the y axis Coordinate System c to d

z1=2-i; % root 1

z2=-2+i; % root 2

z3=-1+2i; % root 3

z4=1-2i; % root 4

lmax=20;

r=ones(n,m); % Setting a n*m matrix to be all 1

for j=1:n

for k=1:m

z=x(k)+i*y(n-j+1); % Generating the complex number, Note n-j+1

if z == 0;

z = tol;

endif

for l = 1:lmax % Newton iteration

zz = (3*z^4+8*i*z^2+25)/(4*z^3+16*i*z); % Newton's Formula for Iteration

if abs(z-zz) < tol

if abs(z-z1) < tol

r(j,k) =1; %Red

elseif abs(z-z2)

r(j,k) =55; %Pink

elseif abs(z-z3) r(j,k) =33; %Light Blue

elseif abs(z-z4) < tol

r(j,k) = 42; %Deep Blue

endif

break

else

z=zz;

endif

endfor

endfor

endfor

colormap('hsv')

image(r)

axis square

axis off