Last week the NY Times ran an article about how some physics professor was analyzing allegedly genuine Jackson Pollock paintings by using "fractal geometry". One line reads: << In previous years Dr. Taylor examined 14 indisputably authentic Pollock paintings by using what is known as fractal geometry, or looking for patterns that recur on finer and finer magnifications, like those in snowflakes.

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This is the first that I heard that snowflakes have patterns that recur on finer and finer magnifications. Needless to say, many interesting fractals can be constructed from recursive algorithms that do in fact end up with identical patterns on finer and finer scales. But I hadn't heard this is a necessary ingredient of a fractal shape. (Technically, there seems to be no fixed definition of a fractal. Everyone agrees that a subset of say the plane having fractional Hausdorff dimension is a fractal. But there are also subsets that have Hausdorff dimension = 1 that most agree should also be called fractals. (E.g., starting with one solid square, divide each (remaining) square into a 2x2 pattern of half-size squares, and discard the NW and SE ones. Then divide each (remaining) square each into a 2x2 pattern, but this time discard the SW and NE ones for each 2x2 pattern. Iterate indefiniitely. The limiting set has Hausdorff dim = 1.) 1, Is This True About (real) Snowflakes??? 2, Does Every Fractal have (in some sense) Repeating Patterns at Finer & Finer Scales? --Dan