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Fractals FAQ



Frequently Asked Questions about Fractal images, software, algorithms, definitions, and reference.

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 ...









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