Mu-Ency - The Encyclopedia of the Mandelbrot Set

The Nucleolus of a second-order embedded Julia 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.

More Pictures:

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.

You can look up specific articles in the index, or see what's new in the changelog.

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

Iterations: 10000

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:".)

footnotes

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.

Mu-ency main page — index — recent changes — DEMZ

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Jul 23.

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