# domain_coloringΒΆ

Visualize a complex-valued function

```import numpy as np
import gr

def domain_colors(w, n):
H = np.mod(np.angle(w) / (2 * np.pi) + 1, 1)
m = 0.7
M = 1
isol = m + (M - m) * (H * n - np.floor(H * n))
modul = np.absolute(w)
Logm = np.log(modul)
Logm = np.nan_to_num(Logm) * n / (2 * np.pi)
modc = m + (M - m) * (Logm - np.floor(Logm))

V = modc * isol
S = 0.9 * np.ones_like(H, float)
HSV = np.dstack((H, S, V))

return HSV

def func_vals(f, re, im,  N):
# evaluates the complex function at the nodes of the grid
# re and im are tuples defining the rectangular region
# N is the number of nodes per unit interval
l = re[1] - re[0]
h = im[1] - im[0]
resL = N * l  # horizontal resolution
resH = N * h  # vertical resolution
x = np.linspace(re[0], re[1], resL)
y = np.linspace(im[0], im[1], resH)
x, y = np.meshgrid(x, y)
z = x + 1j * y
w = f(z)
return w

def plot_domain(color_func, f, re=(-1, 1), im=(-1, 1), N=100, n=15):
w = func_vals(f, re, im, N)
domc = color_func(w, n) * 255
width, height = domc.shape[:2]
domc = np.append(domc, np.ones((width, height, 1)) * 255, axis=2)
domc = domc.astype(np.uint8)
domc = domc.view('<i4')
gr.clearws()
gr.setviewport(0, 1, 0, 1)
gr.drawimage(0, 1, 0, 1, width, height, domc, model=gr.MODEL_HSV)
gr.updatews()

def f(z):
return (z**2 - 1) * (z - 2 - 1j)**2 / (z**2 + 2 + 2j)

for n in range(5, 30):
plot_domain(domain_colors, f, re=(-3, 3), im=(-3, 3), n=n)
```