Frequently Asked Questions about Fractals.

This FAQ about Fractals was compiled and written by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

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This document is provided as is without any express or implied warranty.

Contacting the editors

If you would like to contact the editors, you may do so in writing at the following addresses:

Attn: Michael Taylor

Computing Services

Mount Allison University

49A York Street

Sackville, New Brunswick E4L 1C7

CANADA

email: fractal-faq@mta.ca

- 01 I am new to sci.fratals. What should I know about being online?
- There are a couple of common mistakes people make, posting ads,...

- 02 I want to learn about fractals. What should I read/view first?
- Chaos: Making a New Science, by James Gleick, is a good ...

- 03 What is a fractal? What are some examples of fractals?
- A fractal is a rough or fragmented geometric shape that can ...

- 04 What is chaos?
- Chaos is apparently unpredictable behavior arising in ...

- 05 Are fractals and chaos synonymous?
- No. Many people do confuse the two domains because books ...

- 06 Are there references to fractals used as financial models?
- Most references are related to chaos being used as a model ...

- 07 What is fractal dimension? How is it calculated?
- A common type of fractal dimension is the Hausdorff-...

- 08 What is topological dimension?
- Topological dimension is the normal idea of dimension; ...

- 09 What is a strange attractor?
- A strange attractor is the limit set of a chaotic trajectory. ...

- 10 What is the Mandelbrot set?
- The Mandelbrot set is the set of all complex c such ...

- 11 How is the Mandelbrot set actually computed?
- The basic algorithm is: For each pixel c, start with z = 0....

- 12 Why do you start with z = 0?
- Zero is the critical point of z = z^2 + c, that is, a ...

- 13 What are the bounds of the Mandelbrot set? When does it diverge?
- The Mandelbrot set lies within |c| <= 2. If |z| exceeds 2, ...

- 14 How can I speed up Mandelbrot set generation?
- See the information on speed below (see Fractint). Also see:...

- 15 What is the area of the Mandelbrot set?
- Ewing and Schober computed an area estimate using 240,000 ...

- 16 What can you say about the structure of the Mandelbrot set?
- Most of what you could want to know is in Branner's article ...

- 17 Is the Mandelbrot set connected?
- The Mandelbrot set is simply connected. This follows from ...

- 18 What is the Mandelbrot Encyclopedia?
- The Mandelbrot Encyclopedia is a web page by Robert ...

- 19 What is the dimension of the Mandelbrot Set?
- The Mandelbrot Set has a dimension of 2. The Mandelbrot ...

- 20 What are the seahorse and the elephant valleys?
- The Mandelbrot set being the most famous fractal, its ...

- 21 What is the difference between the Mandelbrot set and a Julia set?
- The Mandelbrot set iterates z^2 + c with z starting at 0 ...

- 22 What is the connection between the Mandelbrot set and Julia sets?
- Each point c in the Mandelbrot set specifies the ...

- 23 How is a Julia set actually computed?
- The Julia set can be computed by iteration similar to ...

- 24 What are some Julia set facts?
- The Julia set of any rational map of degree greater than one ...

- 25 How does complex arithmetic work?
- It works mostly like regular algebra with a couple ...

- 26 How does quaternion arithmetic work?
- quaternions have 4 components (a + i_b + j_c + k_d) ...

- 27 What is the logistic equation?
- It models animal populations. The equation is x -> c x (1 - x),...

- 28 What is Feigenbaum's constant?
- In a period doubling cascade, such as the logistic equation,...

- 29 What is an iterated function system (IFS)?
- If a fractal is self-similar, you can specify mappings ...

- 30 What is the state of fractal compression?
- Fractal compression is quite controversial, with some ...

- 31 How can you make a chaotic oscillator?
- Two references are:...

- 32 What are laboratory demonstrations of chaos?
- Robert Shaw at UC Santa Cruz experimented with chaos ...

- 33 What are L-systems?
- A L-system or Lindenmayer system is a formal grammar ...

- 34 What are sources of fractal music?
- One fractal recording is The Devil's Staircase: Composers ...

- 35 How are fractal mountains generated?
- Usually by a method such as taking a triangle, dividing it ...

- 36 What are plasma clouds?
- They are a Fractint fractal and are similar to ...

- 38 What are Lyapunov exponents?
- Lyapunov exponents quantify the amount of linear stability ...

- 39 How can Lyapunov exponents be calculated?
- For the common periodic forcing pictures, the ...

- 40 Where can I get fractal T-shirts, posters and other items?
- One source is Art Matrix, P.O. box 880, Ithaca, New York,...

- 41 How can I take photos of fractals?
- Noel Giffin gets good results with the following setup: Use ...

- 42 What are the rendering methods commonly used for 256-colour fractals?
- The simplest form of rendering uses escape times. Pixels ...

- 43 How does rendering differ for true-colour fractals?
- The problem with true-colour rendering is that computers use ...

- 44 How can 3-D fractals be generated?
- A common source for 3-D fractals is to compute Julia sets ...

- 45 What is Fractint?
- Fractint is a very popular freeware (not public domain)...

- 46 How does Fractint achieve its speed?
- Fractint's speed (such as it is) is due to ...

- 49 Where can I obtain software packages to generate fractals?
- Stand alone ...

- 50 Where can I obtain software packages to generate fractals?
- Miscellaneous ...

- 52 Where can I obtain software packages to generate fractals?
- For MS-Windows:...

- 54 Where can I obtain software packages to generate fractals?
- For SunView:...

- 55 Where can I obtain software packages to generate fractals?
- For X windows :...

- 56 Where can I obtain software packages to generate fractals?
- Distributed X systems:...

- 57 How does anonymous ftp work?
- Anonymous ftp is a method of making files available to ...

- 58 What if I can't use ftp to access files?
- If you don't have access to ftp because you are on a UUCP,...

- 60 Where are fractal pictures archived?
- Many fractal creators have personal web pages showing images, tutorials......

- 61 Where are fractal pictures archived?
- Sylvie Gallet ...

- 62 How do I view fractal pictures from alt.binaries.pictures.fractals?
- A detailed explanation is given in the alt.binaries....

- 63 Where can I obtain papers about fractals?
- There are several Internet sites with fractal papers: There ...

- 64 How can I join fractal mailing lists?
- There are now 4 mailing lists devoted to fractals....

- 65 What is complexity?
- Emerging paradigms of thought encompassing fractals, chaos,...

- 66 What are some general references on fractals, chaos, and complexity?
- Some references are:...

- 67 What are some general references on fractals, chaos, and complexity?
- E. Ott, Chaos in dynamical systems, Cambridge University Press,...

- 68 What are some relevant journals? (Fractal)
- Some relevant journals are:...

- 69 What are some other Internet references? (Fractal)
- Some other Internet references:...

- 70 What are multifractals?
- It is not easy to give a succinct definition of multifractals....

- 71 What is aliasing?
- In computer graphics circles, aliasing refers to ...

- 72 What does aliasing have to do with fractals?
- Fractals, are very strange objects indeed. Because they ...

- 73 How Do I "Anti-Alias" Fractals?
- We can't eliminate aliasing entirely from a fractal but we ...

- 74 Ideas for science fair projects? (Fractal)
- You should check with your science teacher about any ...

- 76 Who has contributed to the sci.fractals FAQ?
- Former editors, participants in the Usenet group sci....

- 77 Copyright? (sci.fratals)
- This document, sci.fractals FAQ, is Copyright © 1997-1998 ...