sum 1/f(noise)

The picture on the left looks a lot more interesting than the previous picture of a number of reasons. The major reason is that it uses a texture that consists of a fractal sum of noise calls:

  noise(p) + ½ noise(2p) + ¼ noise(4p) ...

We continue this sum until the size of the next term would become too small to see (ie: the noise would fluctuate faster than about once every two pixels). This results in a logarithmically greater cost than simple noise, depending on image resolution.

For example, in the image on the left I needed to use 8 evaluations in the sum, since any detail smaller than (0.5)8 of the image width would just have contributed random noise to the texture at this resolution.

In the example on the left, a simulation of cloud cover over a watery planet, I used this expression to modulate between the white cloud cover and the dark green-blue planet.

The appearance of a thick transparent atmosphere layer is just a trick - I lighten the planet color beyond a certain radius in the image. Then I apply the cloud texture over this, which creates an illusion that this color modulation is in 3D. The planet then appears to be transparent, with a smaller sphere floating within.