Contour Lines

How the image is created

1. generate a regular grid of x and y positions

2. define x/y positions and widths of several hills

3. calculate the height of the hills as a Gaussian Mixture using the positions as means and the widths as standard deviations of a normal distribution, both for x and y separately

4. sum up the hills

5. scale and round the height to regular steps

You can put in any number of hills.

import numpy as np
from PIL import Image


# create a 400 x 400 grid
dim = np.linspace(-10, 10, 400)
x, y, _ = np.meshgrid(dim, dim, [1])  # the [1] adds an extra dimension

# positions and widths of the 'hills'
position_x = np.array([-3.0, 7.0, 9.0])     
position_y = np.array([0.0, 8.0, -9.0]) 
width_x = np.array([5.3, 8.3, 4.0]) 
width_y = np.array([6.3, 5.7, 4.0])

# calculate height as a combination of Gaussians
d = np.sqrt(((x - position_x) / width_x) ** 2 + ((y - position_y) / width_y) ** 2)
z = np.exp(-d ** 2)  # shape is (400, 400, 3) because we have 3 hills


z = z.sum(axis=2)   # add the hills to get a single landscape
znorm = (z - z.min()) / (z.max() - z.min()) # normalize to range (0.0 .. 1.0)

# contour lines
contour = (znorm * 8).astype(np.uint8) * 32
im = Image.fromarray(contour, mode='L')
im.save('contour_steps.png')

# isolines
isolines = ((znorm * 100).round() % 16) == 0
isolines = (isolines * 255).astype(np.uint8)
im = Image.fromarray(isolines, mode='L')
im.save('contour_isolines.png')

Lines only

With a modulo instead of the rounded steps you get to see the contour lines or isolines:

Challenge

Generate random hill centers + sizes.