Plot circular gradients using numpy

I have a code for plotting radial gradients with numpy. So far it looks like this:

import numpy as np
import matplotlib.pyplot as plt

arr = np.zeros((256,256,3), dtype=np.uint8)
imgsize = arr.shape[:2]
innerColor = (0, 0, 0)
outerColor = (255, 255, 255)
for y in range(imgsize[1]):
    for x in range(imgsize[0]):
        #Find the distance to the center
        distanceToCenter = np.sqrt((x - imgsize[0]//2) ** 2 + (y - imgsize[1]//2) ** 2)

        #Make it on a scale from 0 to 1innerColor
        distanceToCenter = distanceToCenter / (np.sqrt(2) * imgsize[0]/2)

        #Calculate r, g, and b values
        r = outerColor[0] * distanceToCenter + innerColor[0] * (1 - distanceToCenter)
        g = outerColor[1] * distanceToCenter + innerColor[1] * (1 - distanceToCenter)
        b = outerColor[2] * distanceToCenter + innerColor[2] * (1 - distanceToCenter)
        # print r, g, b
        arr[y, x] = (int(r), int(g), int(b))

plt.imshow(arr, cmap='gray')
plt.show()

Is there any way to optimize this code with numpy functions and improve speed? It should look like this afterwards:

You can use vectorization to very efficiently calculate the distance without the need for a for-loop:

x_axis = np.linspace(-1, 1, 256)[:, None]
y_axis = np.linspace(-1, 1, 256)[None, :]

arr = np.sqrt(x_axis ** 2 + y_axis ** 2)

or you can use a meshgrid:

x_axis = np.linspace(-1, 1, 256)
y_axis = np.linspace(-1, 1, 256)

xx, yy = np.meshgrid(x_axis, y_axis)
arr = np.sqrt(xx ** 2 + yy ** 2)

and interpolate between inner and outer colors using broadcasting again

inner = np.array([0, 0, 0])[None, None, :]
outer = np.array([1, 1, 1])[None, None, :]

arr /= arr.max()
arr = arr[:, :, None]
arr = arr * outer + (1 - arr) * inner