 # Fractals FAQ

This FAQ about Fractal images, software, algorithms, definitions, and reference. was compiled and written by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by others. 1: I want to learn about fractals. What should I read/view first?
_Chaos_ is a good book to get a general overview and history. _Fractals ... 2: What is a fractal? What are some examples of fractals?
A fractal is a rough or fragmented geometric shape that can be ... 3: What is chaos?
Chaos is apparently unpredictable behavior arising in a deterministic ... 4a: What is fractal dimension? How is it calculated?
A common type of fractal dimension is the Hausdorff-Besicovich ... 4b: What is topological dimension?
Topological dimension is the normal idea of dimension; a point has ... 5: What is a strange attractor?
A strange attractor is the limit set of a chaotic trajectory. A strange ... 6a: What is the Mandelbrot set?
The Mandelbrot set is the set of all complex c such that ... 6b: How is the Mandelbrot set actually computed?
The basic algorithm is: ... 6c: Why do you start with z=0?
Zero is the critical point of z^2+c, that is, a point where ... 6d: What are the bounds of the Mandelbrot set? When does it diverge?
The Mandelbrot set lies within |c|<=2. If |z| exceeds 2, the z sequence ... 6e: How can I speed up Mandelbrot set generation?
See the information on speed below (see Fractint). Also see: ... 6f: What is the area of the Mandelbrot set?
Ewing and Schober computed an area estimate using 240,000 terms of the ... 6g: What can you say about the structure of the Mandelbrot set?
Most of what you could want to know is in Branner's article in _Chaos ... 6h: Is the Mandelbrot set connected?
The Mandelbrot set is simply connected. This follows from a theorem ... 7a: What is the difference between the Mandelbrot set and a Julia set?
The Mandelbrot set iterates z^2+c with z starting at 0 and varying c. ... 7b: What is the connection between the Mandelbrot set and Julia sets?
Each point c in the Mandelbrot set specifies the geometric structure of ... 7c: How is a Julia set actually computed?
The Julia set can be computed by iteration similar to the Mandelbrot ... 7d: What are some Julia set facts?
The Julia set of any rational map of degree greater than one is perfect ... 8a: How does complex arithmetic work?
It works mostly like regular algebra with a couple additional formulas: ... 8b: How does quaternion arithmetic work?
Quaternions have 4 components (a+ib+jc+kd) compared to the two of ... 9: What is the logistic equation?
It models animal populations. The equation is x -> c*x*(1-x), where x ... 10: What is Feigenbaum's constant?
In a period doubling cascade, such as the logistic equation, consider ... 11a: What is an iterated function system (IFS)?
If a fractal is self-similar, you can specify mappings that map the ... 11b: What is the state of fractal compression?
Fractal compression is quite controversial, with some people claiming ... 12a: How can you make a chaotic oscillator?
Two references are: ... 12b: What are laboratory demonstrations of chaos?
Robert Shaw at UC Santa Cruz experimented with chaos in dripping ... 13: What are L-systems?
A L-system or Lindenmayer system is a formal grammar for ... 14: What is some information on fractal music?
One fractal recording is The Devil's Staircase: Composers and ... 15: How are fractal mountains generated?
Usually by a method such as taking a triangle, dividing it into 3 ... 16: What are plasma clouds?
They are a Fractint fractal and are similar to fractal mountains. ... 17a: Where are the popular periodically-forced Lyapunov fractals described?
See: 17b: What are Lyapunov exponents? 17c: How can Lyapunov exponents be calculated?
For the common periodic forcing pictures, the lyapunov exponent is: ... 18: Where can I get fractal T-shirts and posters?
One source is Art Matrix, P.O. box 880, Ithaca, New York, 14851, 1- ... 19: How can I take photos of fractals?
Noel Giffin gets good results with the following setup: ... 20: How can 3-D fractals be generated?
A common source for 3-D fractals is to compute Julia sets with ... 21a: What is Fractint?
Fractint is a very popular freeware (not public domain) fractal ... 21b: How does Fractint achieve its speed?
Fractint's speed (such as it is) is due to a combination of: ... 22a: Where can I obtain software packages to generate fractals?
For X windows: ... 22b: What are some supporting software/utilities? (Fractal)
Some supporting software/utilities/sources are: ... 23a: How does anonymous ftp work?
Anonymous ftp is a method of making files available to anyone on ... 23b: What if I can't use ftp to access files?
If you don't have access to ftp because you are on a uucp/Fidonet/etc ... 24a: Where are fractal pictures archived? 24b: How do I view fractal pictures from alt.binaries.pictures.fractals?
A detailed explanation is given in the alt.binaries.pictures FAQ ... 25: Where can I obtain fractal papers?
There are several Internet sites with fractal papers: ... 26: How can I join the BITNET fractal discussion?
There is a fractal discussion on BITNET that uses an automated mail ... 27: What is complexity?
Emerging paradigms of thought encompassing fractals, chaos, ... 28a: What are some general references on fractals, chaos, and complexity?
Some references are: ... 28b: What are some relevant journals? (Fractal)
Some relevant journals are: ... 29: Are there any special notices? (Fractal)
NOTICE (from Michael Peters): ... 30: Who has contributed to the Fractal FAQ?
Participants in the Usenet group sci.fractals and the listserv forum frac-l ... 31: Copyright? (Fractal)
Copyright (c) 1995 Ermel Stepp; 1994, 1993 Ken Shirriff ...