Mu-Ency - The Encyclopedia of the Mandelbrot Set
This is a picture from the Mandelbrot Set, one of the most well-known fractal images in the world. (Click it for a larger version). The Mandelbrot Set is one of my hobbies, and I have collected a large amount of information about it. To organize that information I have created Mu-Ency, a large collection of text files linked to each other1.
Here are some entries from Mu-Ency:
- Mandelbrot Set: The mathematical definition.
- History: How the Mandelbrot Set was discovered, how it became popular, etc.
- Exploring: The many things you can expect to find when you explore on your own.
- Area: I have been involved in finding the area of the Mandelbrot Set. Here are the latest results.
- Algorithms: How to compute the Mandelbrot Set and how to draw it.
- R2 Naming System: I have also developed a rather precise (and complex) naming system for features of the Mandelbrot Set. Mu-Ency presents many examples of this naming system.
Some entries with pictures of parts of the Mandelbrot Set are: R2, Cusp, Embedded Julia set, 2-fold Embedded Julia set, 4-fold Embedded Julia set, Paramecia, R2.C(0), R2.C(1/3), R2.1/2.C(1/2), R2t series, Seahorse Valley, Delta Hausdorff Dimension, Exponential Map, Color, Representation Function, Reverse Bifurcation.
... or just explore on your own using DEMZ.
Coordinates of the image above:
Center: -1.769 110 375 463 767 385 + 0.009 020 388 228 023 440 i
Width (and height): 0.000 000 000 000 000 160
Algorithm: distance estimator
An ASCII art Mandelbrot set: vL , '*m-` -m/**\a, ... _,/#, ]),., ., '#F-.F~*^' '`'*~*eae/: . -__/* '`_* )_. ic,_ ./- T\a 7F*-~~*a, /` dL \_,\F^ '\` .*` .,___\____._/*^* R2a .m~ ` ' :*r(, . ~e ` -\r._____/`L @e _-**^)~*' ]c .^_ -~ ` .)L_, _-`' .]F_.,, ,.-e_@, -*#^ *~*v- '-/-~* '`]- d@,,..(, ^'*m-' i*^^` '^` (If you like fractal ASCII art, there is more at most of the pages listed above at "More Pictures:".)
1 : "text files linked to each other" : Mu-Ency began as a glossary in 1988, intended to be accessed by sending commands by email message to a server that sends plain-text responses. Its source language remains in RHTF, my human-friendly style annotation like Markdown but far more capable.
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Jul 23. s.27