Robert P. Munafo, 1999 Feb 2.
There are many methods of improving the speed (performance) of a program which generates views of the Mandelbrot Set. Most of them are described in this encyclopedia.
The following table is a heirarchical listing of categories and algorithms, each of which is described fully under its own heading. Some are deliberately listed twice.
. . Approximation
. . . . Integer Math
. . . . Low Resolution
. . . . Low Dwell Limit
. . Ideal Parameter Selection
. . . . Automatic Dwell Limit, heuristic method
. . . . Automatic Math-Precision
. . . . Runtime Benchmarking
. . Optimization: changing the algorithm
. . . . Orbit-Based Optimization (exploit orbital dynamics)
. . . . . . Orbit Detection
. . . . . . Perturbation Methods
. . . . . . . Synchronous-Orbit Algorithm
. . . . . . Common Ancestors method (Julia Sets only)
. . . . . . Inverse Iteration method (Julia Sets only)
. . . . Adjacency Optimization (exploit local similarity)
. . . . . . Successive Refinement
. . . . . . Boundary Scanning
. . . . . . Mariani/Silver Algorithm (rectangle subdivision)
. . . . . . Circle Tiling (using distance estimator)
. . . . . . certain other methods described under Adjacency Optimization
. . . . . . Exponential Map
. . Successive Tradeoff Methods
. . . . Successive Refinement
. . . . Successive Dwell Limit
. . . . Limited-Region Refinement
Many of these methods work by presenting an improved user interface, in which browsing is easier and faster. Other methods use traditional optimization techniques: smart algorithms, approximations that introduce negligible error, etc. A few, most notably Successive Refinement, do both.
revisions: 19990202 oldest on record; 20101205 Add link to exponential map
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Aug 09. s.27