Fractals FAQ

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 ...