After some experimentation i found that this can occur with both the L1 and L2 norms (i was expecting it to be more likely for the L1 norm, but this seems not to be the case). It seems to occur when the algorithm wanders into territory where there is a lack of good fits in the input texture. This might occur if the input texture is too small or not sufficiently homogeneous.
Note the similarity to the repeating cycles and randomness that frame the edge of chaos. Best-fit synthesis is somewhat similar to cellular automatons, with the rule set defined by the input texture. Told you it was important :-)
I hypothesize that these repeating patterns are analogous to obsessive-compulsive behaviour or repetitive autistic behaviours, and that garbage is analogous to schizophrenic psychosis.
Things that might cause a lack of good fits:
- Mental retardation. A mind that simply does not contain much data.
- An unsuitable environment. An environment designed to suit L2 minds might confuse L1 minds. L1 minds do not make the same types of generalization that L2 minds do.
- A very unusual situation, such that the person has no previous relevant experience.
Note that the last two causes can be solved by modifying the environment, not the person.