This site seems to explain its origins:
http://www.pinningdownautism.com/autism.html
Quote:
The Significance of the Puzzle Piece Image
The puzzle piece logo was first created in 1963 by the National Autistic Society. They explain “that the symbol of the Society should be the puzzle as this did not look like any other commercial or charitable one as far as they could discover. The puzzle piece is so effective because it tells us something about autism: our children are handicapped by a puzzling condition; this isolates them from normal human contact and therefore they do not 'fit in'.”
Since then, the interlocking, mutli-colored puzzle piece has become the international symbol of autism. Its significance has become multi-faceted. For some it represents the mystery and complexity of the disorder, for others it represents the mechanical nature of an autistics persons thought process. The bright colors are said to represent hope.
(Bolding emphasis mine.)
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clarity of thought before rashness of action