The Mariani-Silver Algorithm for Drawing the Mandelbrot Set

What is the Mariani-Silver Algorithm?

Why is it called the Mariani-Silver Algorithm?

Why does it (mostly) work?

  • p(0) =c
  • p(1) = c²+c
  • p(2) = (c²+c)²+c
  • p(3) = ((c²+c)²+c)²+c
  • etc.
  • I didn’t have a proof for Part 2 back then
  • Rollo provided a proof a few weeks after I wrote him
  • I understood his proof well enough, it was obviously correct, I suspect he shared it with Dewdney and others, I recall it being pretty simple
  • I don’t remember Rollo’s proof, so I’m going to offer you my own proof of Part 2, however
  • it’s entirely possible, even likely, that although I don’t remember Rollo’s proof that it’s still rattling around my head somewhere and what I’m about to do is repeat Rollo’s proof
  • on the other hand, I might botch this next bit in which case any mistakes are mine
  • only Rollo could tell me if this was his proof or not
  1. R does not overlap M(i+1) at all
  2. R partly intersects with M(i+1)
  3. R completely contains M(i+1)

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I’m a software engineer at Facebook; I specialize in software performance engineering and programming tools generally. I survived Microsoft from 1988 to 2017.

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Rico Mariani

Rico Mariani

I’m a software engineer at Facebook; I specialize in software performance engineering and programming tools generally. I survived Microsoft from 1988 to 2017.

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