There is no single correct way to define a “random” texture. We
would certainly expect it to be isotropic and, in the absence of tone
variation, evenly-spaced. Seeking inspiration in other work, we
note that Berg [2001] uses a coral-like random texture for rough,
natural shapes such as terrain and stones. This texture is reminiscent
of reaction-diffusion patterns [Turk 1991], and reproduced by
the geometric attraction-repulsion algorithm of Singh and Pedersen
[2006].
Our random maze texture is very simple. We build a grid by taking
the intersection of a regular square grid with the region. We
then immediately build a maze using the algorithm of Section 5.
Afterwards, we randomize the square maze in a post-process by
passing it through Singh and Pedersen’s algorithm. The result is a
maze with the random appearance of their results, but with branching
walls and maze structure. A simple example is presented in
Figure 7.
Note that because it is a post-process, the relaxation algorithm can
also be used to “loosen up” directional and spiral mazes to any desired
degree. Relaxation can help suppress occasional artifacts in
these other textures, such as passages that are too narrow