![]() For example, the meandering point is more likely to strike a spike in the Julia set that juts out into the plane than it is to intersect with a crevice tucked into a region of the set. The MME is a way of quantifying the fact that the meandering point is more likely to strike certain parts of the Julia set than others. Wherever it first strikes the Julia set is where it comes to rest. From that distant location the point is going to take a random walk across two-dimensional space, meandering until it strikes the Julia set. Then picture a point on the same plane but very far outside the Julia set’s boundary (infinitely far, in fact). First, picture a two-dimensional filled Julia set on the plane. The MME is a complicated concept, but there is an intuitive (if slightly incomplete) way to think about it. All Julia sets have what’s known as a “measure of maximal entropy,” or MME. A unique attribute of Julia sets allows DeMarco and Lindsey to know the curvature of the shapes they’re building.
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