# Speed Improvements

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.

Speed Improvements

. . 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.

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