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Miloslav Ciz 2025-05-03 16:21:08 +02:00
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mandelbrot_set.md
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@ -86,7 +86,7 @@ Mandelbrot set is similar and related to **[Julia sets](julia_set.md)**; in a wa
The following are some **attributes** of the Mandelbrot set:
- **[Hausdorff dimension](hausdorff_dimension.md)** (of the boundary): 2
- **area**: approximately 1.5052; this is a current best estimate, the area is not easy to calculate (it may be estimated e.g. with [Monte Carlo](monte_carlo.md) methods).
- **area**: approximately 1.5052; this is currently the best estimate, the area is not easy to calculate (it may be estimated e.g. with [Monte Carlo](monte_carlo.md) methods).
- It is **symmetric** along the *x* axis.
- It's proven the set is **connected**, i.e. it's just a single "island".
- The number [pi](pi.md) is embedded in the shape of the set in a hugely mysterious way which was discovered by mistake by David Bolle in 1991 who tried to measure the width of the gap touching the point [-0.75,0] -- as he increased precision of his iterative algorithm, the number of iterations started to approximate digits of pi.