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. ...

- 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 ...

- 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 ...