2D [systems based on] constraints

The constraints shown here are minimal, in the sense that in each case removing any of the allowed templates prevents the constraint from ever being satisfied. Note that constraints which differ only by overall rotation, reflection or interchange of black and white are not explicitly shown. The number of allowed templates out of the total of 32 possible varies from 1 to 15 for the constraints shown, with 12 being the most common. Smaller sets of allowed templates typically seem to lead to constraints that can be satisfied by visually simpler patterns.