computer science, programming and other ideas

Hi everyone, I have written an implementation of Perlin noise with numpy that is pretty fast, and I want to share it with you. The code is available here.

My code looks like the original implementation. The only difference is that I tried to use the vectorized operations of numpy as much as possible instead of `for`

loops. Because as you may know, loops are really slow in Python.

Here is the code:

```
def generate_perlin_noise_2d(shape, res):
def f(t):
return 6*t**5 - 15*t**4 + 10*t**3
delta = (res[0] / shape[0], res[1] / shape[1])
d = (shape[0] // res[0], shape[1] // res[1])
grid = np.mgrid[0:res[0]:delta[0],0:res[1]:delta[1]].transpose(1, 2, 0) % 1
# Gradients
angles = 2*np.pi*np.random.rand(res[0]+1, res[1]+1)
gradients = np.dstack((np.cos(angles), np.sin(angles)))
g00 = gradients[0:-1,0:-1].repeat(d[0], 0).repeat(d[1], 1)
g10 = gradients[1:,0:-1].repeat(d[0], 0).repeat(d[1], 1)
g01 = gradients[0:-1,1:].repeat(d[0], 0).repeat(d[1], 1)
g11 = gradients[1:,1:].repeat(d[0], 0).repeat(d[1], 1)
# Ramps
n00 = np.sum(grid * g00, 2)
n10 = np.sum(np.dstack((grid[:,:,0]-1, grid[:,:,1])) * g10, 2)
n01 = np.sum(np.dstack((grid[:,:,0], grid[:,:,1]-1)) * g01, 2)
n11 = np.sum(np.dstack((grid[:,:,0]-1, grid[:,:,1]-1)) * g11, 2)
# Interpolation
t = f(grid)
n0 = n00*(1-t[:,:,0]) + t[:,:,0]*n10
n1 = n01*(1-t[:,:,0]) + t[:,:,0]*n11
return np.sqrt(2)*((1-t[:,:,1])*n0 + t[:,:,1]*n1)
```

If you are familiar with Perlin noise, nothing should surprise you. Otherwise, I can suggest you to read the first pages of this article which explains Perlin noise very well in my opinion.

An example of what the function generates:

I normalized the gradients so that the noise is always between -1 and 1.

Using the previous function, I wrote another that combines several octaves of Perlin noise to generate fractal noise:

```
def generate_fractal_noise_2d(shape, res, octaves=1, persistence=0.5):
noise = np.zeros(shape)
frequency = 1
amplitude = 1
for _ in range(octaves):
noise += amplitude * generate_perlin_noise_2d(shape, (frequency*res[0], frequency*res[1]))
frequency *= 2
amplitude *= persistence
return noise
```

An example of what we can obtain:

The fractal noise is not always between -1 and 1 but between -2 and 2 if you keep the persistence equals to 0.5.

I will show you in future articles how I used Perlin noise and fractal noise in my projects.

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