November 22nd, 2004

eyes black and white

The Garden of Forking Paths

Collapse ) Thus, just like everyone else a few decades ago, I've finally come to fascinatedly watch the Mandelbrot set for hours, and I have tried to understand the patterns or its self-similarity. Below are the conjectures that I've made while watching Xaos draw the Mandelbrot set in high resolution, letting it zoom in and out at random, or zooming manually to check out some idea. I suppose these conjectures are all well-known by now, and probably also proven already, at least based upon some other more interesting mathematical conjectures. But I really don't feel like digging the mathematical litterature about it, so instead I'll bleg those of you who know to point me to proper documents that summarize the knowledge about these patterns and more. (If I were web connected while writing this, I'd Google for it; but then again, if I had an Internet connection, I wouldn't be writing this to begin with.)

Collapse )