Cool Tile-Generation inspired by Quantum Mechanics: Wave Function Collapse.
Local similarity means that
- (C1) Each NxN pattern of pixels in the output should occur at least once in the input.
- (Weak C2) Distribution of NxN patterns in the input should be similar to the distribution of NxN patterns over a sufficiently large number of outputs. In other words, probability to meet a particular pattern in the output should be close to the density of such patterns in the input.
In our examples typical value of N is 3.
WFC initializes output bitmap in a completely unobserved state, where each pixel value is in superposition of colors of the input bitmap (so if the input was black & white then the unobserved states are shown in different shades of grey). The coefficients in these superpositions are real numbers, not complex numbers, so it doesn't do the actual quantum mechanics, but it was inspired by QM.
Also does its thing in 3D:
These voxel models were generated with N=2 overlapping tiled model using 5x5x5 and 5x5x2 blocks and additional heuristics.