Mu-Ency History

Robert P. Munafo, 2009 Jan 21.

This page contains some old text from the early days of mu-ency, and related material mainly only of interest to me.

19930310 ReadMe

ReadMe for Munafo's Mandelbrot Set Glossary and Encyclopedia

Robert P. Munafo, 1993 Mar 10.

From the Mandelbrot Set Glossary amd Encyclopedia. Usage of this material is subject to the terms and conditions of the GNU``General Public License.

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The Mandelbrot Set Glossary and Encyclopedia (hereafter called "Mu-Ency") is a collection of text files covering dozens of topics related to the Mandelbrot Set. It is intended to be as complete as possible, and is under continuous revision. It is written for readers with experience in mathematics equivalent to college freshman calculus.

Content

One central purpose of Mu-Ency is to present a naming system (The "R2" system) which can be used to specify features of the Mandelbrot Set in a non-ambiguous manner. This naming system, while complex, is greatly preferable to the use of coordinates because it allows serious Mandelbrot explorers to apply organization to the many, many images they view. It is by far the most comprehensive such system yet developed.

Mu-Ency includes much material relating to computer programming. Exploring the Mandelbrot Set requires rather complex programs, because the simple algorithm (compute and plot each pixel) is much too slow for interactive browsing.

Format

Mu-Ency is a set of plain ASCII text files. Each has an identifying name called the heading, by which it is referred in cross-references. Each file is an "article" styled after the entries in an encyclopedia. There are many cross-references but (as yet) no index. There are many illustrations, also in text format. Views of the Mandelbrot Set have been converted to text using a reasonably sophisticated pattern-matching algorithm.

Distribution

Mu-Ency is not complete (much of it is in non-portable Macintosh format) and is currently available in pieces from the author. Send E-mail to:

mandel@vgi.com

and you should get a response within a day. Eventually, an automatic server will be running at this address.

If you are still interested after reading this file, send a message asking for a table of contents.

19961030 ReadMe

ReadMe
for Munafo's Mandelbrot Set Glossary and Encyclopedia

Robert P. Munafo, 1996 Oct 30.

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This file describes Robert Munafo's Mandelbrot Set Glossary amd Encyclopedia, how to get it, and how to use it.

The Mandelbrot Set Glossary and Encyclopedia (hereafter called "Mu-Ency") is a compilation of material from many sources, compiled over many years. It is intended to cover everything that is known about the Mandelbrot Set and which is capable of being understood by those with mathematics ability up to and including college freshman calculus. More complex knowledge is presented using language that can be understood by readers of this level.

Content

One central purpose of Mu-Ency is to present a naming system (The R2 system) which can be used to specify features of the Mandelbrot Set in a non-ambiguous manner. This naming system, while complex, is greatly preferable to the use of coordinates because it allows serious Mandelbrot explorers to apply organization to the many, many images they view. It is by far the most comprehensive such system yet developed.

Sources

The material in Mu-Ency comes from three sources:

- writings of Benoit B. Mandelbrot and other recognized mathematicians (see Bibliography).

- Various individuals on the Internet, including students, teachers, programmers, mathematicians, etc.

- My own observations, analysis and conclusions.

Disclaimer

Mathematical terms and concepts have probably been misused in some instances. This is due primarily to ignorance on my part. I invite more knowledgeable readers to constructively criticize with regard to such errors.

Format

Mu-Ency is a set of plain ASCII text files. Each has an identifying name called the heading, by which it is referred in cross-references.

Each file is an "article" styled after the entries in an encyclopedia.

There are many cross-references but (as yet) no index. There are many illustrations, also in text format. Views of the Mandelbrot Set have been converted to text using a reasonably sophisticated pattern-matching algorithm.

Distribution

Mu-Ency is distributed by electronic mail on the global Internet. An automatic mail daemon at vgi.com receives requests and responds to them. The server responds right after it gets the mail, so your wait time for a response should be about twice the normal delay you get in sending mail to Internet sites in the United States.

To request a copy of this file (the ReadMe), send mail to the address:

munafo@vgi.com

containing the following text in either the Subject: line or the message body:

send mu-ency readme

Upper/lower case is ignored in the request.

To request the table of contents, use either of the following:

send mu-ency contents
send mu-ency table

Once you have received the table of contents, you can request individual entries:

send mu-ency binary decomposition
send mu-ency bin decom
send mu-ency binary
send mu-ency decomp

Each of these examples will return the entry on "Binary Decomposition", note that abbreviations are accepted and not all words are required. However, you should be aware that some abbreviations are not unique. For example, "inte" could refer to "Integer Math" or "Interior Dwell".

Ideas for an interactive web interface for exploring the Mandelbrot Set, which would also cause everything viewed (including, presumably, popular and ininteresting views) to be cached on the server

A possible www interface ~~~~~~~~~~~~~~~~~~~~~~~~ Overview ~~~~~~~~ The goal is to provide a real-time interactive Mandelbrot Set browser program, which can be viewed by anyone through www using a line-oriented (text-only) interface. We assume that only static files with hyperlinks are possible; we also assume that the www program will load a file only if (and when) the user "jumps" to that file. We can make the browser fully interactive without precomputing all of the images by intercepting the file-system requests as they are made by the FTP daemon. When a file is requested, a set of 16 new files are generated (representing the new views that will be accessible from the file just requested). The next FTP file request for one of these 16 files will block until all 16 files are done being generated. (Alternatively, each FTP request for a frame could block while the frame gets drawn. However, this means the users always wait for computation to take place.) Up to 16000 such files will be maintained on the hard disk, then old ones will be deleted in the order that they were created. If an FTP request came through for one of the old files, it could then block while the file is recomputed. Screen Display: ~~~~~~~~~~~~~~~ 23 lines, 79 characters wide. One line for machine and file identification, one line for center and size, and one line for WWW prompt. (We avoid 24 and 80 to allow for wierd terminals, extra UI layers like a more prompt, etc.) mrob.u27.neci.somerville.ma.us://pub/mandel/interact/user1/frame37/f36_choice7 Center: -0.759 +0.402i Width: 2.599 1 -_ 2 "_ ._e 3 [1] [2] [3] .`m"' [4] 4 ._e.,r"r,._ 5 '.Y^' ^\/- 6 , , ,_ ^\, .F` . _, 7 :a\%_,_(*_r--*-- -"--\_"r _, v`, 8 [5] [6] -@,[7]^` [8]_~`(/*- 9 -_m_:-"` -.'" . -c ., .^Y,` ^/. . 1 "\.,c, *`_:_ .TC^ ^^)" 2 dd^Y""""-Ya_ ]F b_, 3 [9] :, -m-'[10] '*,]` [11] [12] b^` 4 "m__/F` '/ ._*` 5 _______"___/____._r~ ^` :~` 6 " ' ' '^)__r, ~e, 7 :"^' -@- _/] '@c 8 [13] ^^%a[14],__._a* ', [15] [16] Cmc 9 ..:7rF"""d^@'` 'Y_ .(__ . T; ` *- ""v, .rv~( 1-16, Up, Back, Help After choosing [6], they would see this: mrob.u27.neci.somerville.ma.us://pub/mandel/interact/user1/frame38/f37_choice6 Center: -1.097 +0.500i Width: 1.299 1 2 3 [1] [2] [3] [4] 4 5 . .__ 6 *Ye,cm' 7 aem'Tmm. 8 [5] [6] [7] [8] `._Y)'^ 9 -YY[, . _. __'%%- 1 v_mF[a_]@"` 2 ._ _ 'T"@^`"~ 3 [9] [10], ,, [11] ._[12] 4 --\, ., 'm-` -m@)-* 5 -"--Lcdr:, ''@e_ ._- _^%- 6 '`%F*/b.-__v""@\,%@e._ "*C^ 7 ^-"@, '"^`^^`'^^^"'"/Yc_ '"C` 8 [13] [14]a,-am*^ [15] ^"Tm_ :@F [16] 9 .. '^*F"" 'Te .F . ^b,. , -vm" '\'- 1-16, Up, Back, Help After choosing [11]: mrob.u27.neci.somerville.ma.us://pub/mandel/interact/user1/frame39/f38_choice11 Center: -0.9647 +0.4095i Width: 0.6500 1 2 3 [1] [2] [3] [4] 4 5 6 _ 7 -aL_vY 8 [5] [6] [7] [8] :/$*F 9-- '^-$" .^--\.-- 1 ,(^ ._ ., 2 '^F-` .'`c, . .7@^_. 3._--`_,[9] [10]r"'` [11] [12]\@@Le@* 4 '"C_ . :, .7 -$c... . . '~")@e, 5 -^')\/"m:-r,.:b- _, ^`'@b_@_ ._/L .__ ^%)" 6 .'F*beF"_ -F` . .,.^\@@@*_ Y^_, ._a$`m(@- 7 '' _`dF"be@@"_ dL._'*-@F^'*@-., ,-/@/L ,., *Y@@`,` 8 [13].-m\d`'`^`*@c:,-[14]m%@, _Cedbe^@*"[15]^%` [16]\T/` 9 ^)e-Y"*^ $_b*^^^' ''^~ -(aeea@@ __, -dC^^` . --*\e__, '` `" d(.\d, _m_@` 1-16, Up, Back, Help

The following is a sequence of ASCII graphics images showing the history of changes to the ASCII graphics generator routine in Power MANDELZOOM. All of these images are from 19921227 or earlier.

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First version: samples one pixel out of each 8x16

** * * * ** ** ** * * * * ** **** * * * ** ** * * ** ** * * *

— — -- —

Decrease cell size to 6x12

* * * * * ** **** ** * * * * * * * * * * * * *** * * * * * * * ** ** * * * ** * * *** ** * * ** * ** *

— — -- —

First 4-bit version. Samples 4 pixels out of each 6x12, uses a lookup table to choose the character to plot:

. \,` ._d~d. # L FF._~~~` '~~'L _)_ _'`' ~ F ', , .( 7_, '#',F)_ F F . 'd` ', 7 _ ,_~~` ' `'( ( . \ ` ~_ , 7, ,/~7,~~ L \, ` .d, .`` .~ . 7_ F7~ . `` `)' 7 d '~~.`' .~~, ~

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Second 4-bit version. Samples 4 blocks out of each 6x12; within each block samples 9 pixels. If any of the nine within the block is dark, the whole block is treated as dark. This was intended to make RF(1/2B1) visible, but it also makes the rest too dark.

'# , )#F` ###7##, .__ ._'# .# . _ )#F##~~~` ~~~~LdL## __#~~ ~_# #(_ d,. dF #LL 7#7####,)F '#, L_7#` ~d .# _________L#~~` .,~ `##7L _ #_ ` ~7L.____F), '#, _F#~#F7~ '#, d#_ ~` ' d#_ d#`` .#F#_ _#_#_ )##~7#~#` 7#~7`'`#~ d#_._#, ~~7#F~ d~~( '~

— — -- —

Third 4-bit version. In each 6x12 cell, the first method is used (only 4 samples) and if the result is totally white then the second method is used (4 x 9 samples). Retains the "lightness" of the first method while showing RF(1/2B1) ; however, there is still a bit of clutter, I think. Differences on RF(1/2B1) probably result from higher resolution in the original image.

'. , )\,` ._d~d., .__ ._'# .L . _ )FF._~~~` '~~'Ld_)_ __'`' ~_F ',_ d,. .( 7_, '#',F)_,)F 'F, ._'d` ', .7 ______.__,_~~` .,' ` ' `'(7( . \_ ` ~~_.____,), '7, _,/~7,~~ 'L, d\, ~` ' .d, d.`` ..~#_ _._7_ )F7~7.~#` 7#~``'`)' d7_._d, '~~.`' .~~, '~

— — -- —

Third algorithm again, on a more typical image.

-.9160 + .2662i @ .0625 7_~#__ ____ )7/L ./77,#,7_ _ ~('d___# )#F## .~~ ''~ '##,_d`, , .L#'7)F', _/_'( ._#('7_ )#_/~ ''~##_(` _ .d#_ '_L .#F#_#_,)d__L7( _ ~7L#, ~~.#_.,d#~_ d~d #,_ '' .d##7L_#.,L_d( __d7` ._____ ._ ~~'d~###F7F`_,, .##___L_F#L#d#7F_LL_\###_~###_(~ 'F/'~dL#7##7`L/~######~,._~F~` ` '/`\d###L##L#F ~###` .___ `._ ____d###_' '~_dF#F7#d_`'~ ,~_._ )L'###~` ~7#,\d7FL \L##L,_ _.##F ~~#d###( _~~##LL_'~7L, )_#~'~` __d, `''F#~#7_`#L .####F~ .#~~~ ' ~~7#L_ __##F`.. ~)#,_, ____~7(_(d#_,._.####. . `~~~`~~'~~~ ~~~~~~~`

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Another test view with algorithm 3.

-.100 666 72 + .956 512 74 i @ .000 008 00 ._~'L _ .#_#,( ~_'d/~ '` _'L'_ '~~L~` ,__~7~ , ._,~L,_ _### '.#~` , , .(\)_ `). _._`` )_ \,(_ .,`L,. ~~L .__~#` ._. __ 77`_,._ )_LL, '\'~` _.,'~,_,~ ~~ )#,#_,, ~~`#_ _ . .~ . .,, ~,\/7`/~` ' .\/`, ._/7,~(7.d__~_ 'LFd(`/' ' )FL 7_'7_~/(#dL,`_`.dL~L`` ._, __._._d._._~\/~d####/~_~~_, _ _LL_//~)F~ .L#~~7FdF`7##7~~~'` , ._./L. '`( ''` _LL__###L__##LdL/___.._L#7#`~## _,.``_/\_7L##~~L~_,`~~.~` ` ., .dLdF~dd~_~()`L~_~_'~ '#F.. ._ 7.\_#~(L 'd/`)`),),7,, )7_,.` 7.7._Fd\, ' .d,' '`'~(__` `'#LF,__ d_~7~_ _,_~L, ~'F#~ ' '~d, _, '` _L,~` 'L_ '.~L_# '~#~ '` _#,,`'` ')L, '~'_~ ,, _,.d/FF F'(` .'\_~` ._d/~, _/L__ '`/L' . , ''''` ~~~` '~ '~`

— — -- —

Method 4. Character-cell size is changed to 5:12 pixels, which is the standard VT-100 aspect ratio (25:80 on a 3:4 screen means (4/80):(3/25) = .05:.12 characters)

7` , ~_~` .__F7L., ._., _,'#, .L , ., )FF7.d`~~' `~~~7,._)L . _,'`' '`_F` \_. ._,_ .d` 7__, ~F'_dLF__ )~ )` .__`F~ '\` '` .,______,_)__F~~ .,' ` ' '(,), d \, ` ~`_.____.,`( ~_ .~\~~L/7' ), .~_, '' ` _L, d.'' ..~)._ .d,_7. .F7F ./~#, .#~'F '`)( d7_,_.d, '~'(_`' .'`~, '`

— — -- —

Method 4 again.

._/`'L,._ .d_dL_` '._\./~ ~ _'\,`_ '~~)d~` ,._d77~` , _,~7_ _ .#)(' '.#/~, , _ )'_7_ d(_ .,,_`'` \, 7,#d_ ..'~_,_, ~~_ _._,~#` .,. ._, ~'F.__._, ._L#_~ '('~' _ _ '\,__~` '~ .#/#,d_ '''`#_, _ .,'#~ _, _. ~,F_7F`/~~ ' //d_, __'#,~('(.#__F.. '7)\((`L`` ` .~# 7_'~_/7/()()./`_~__dLF)d'` .,. __ ___,d.____~7_~(d###FL/~.'~`_,, _ _L#__/d~7FF~ _``~~~#d#F''#L#7~~~~'` , _..,)_, '`7` ''` _\._dd###L__d##L)dd`___ ___L(~)L`~77( _, ____,~_#7F7##F~L/.__`~~~d`` ' _ .d\_F7~__~`_~('F)(7_~L_~~ 'LF _ ., '_/__#~d7_ '._~.)~.L L 7__ )7L_._` ',dL.dF\FL` ` _#, ` ~ ~#___` `)7L_F,._, ._/~F~_ ..__'__ '~#~F~ ' '~.L( __ ~ '_.,~~ 'L_` `d~L_#` '~d'` '7 .d..d``` '',._ ~7'_~ . , _, ,_7~, ~'#~ .'~.,~` __#d`_ ._/F___ '`_7_` ,. '~' ~` ~~`~` ~` ~~

— — -- —

Method 5: Each 5x12 cell is now divided into 6 blocks, 2x4 pixels in size (the rightmost column of the 5x12 is ignored entirely). 6 bits per character can thus be expressed. "^" replaces "~" as the character of choice for the top of the cell; "@" replaces "#" as the "all black" character.

vL , '*m-` -m/**\a, ... _,/#, ]),., ., '#F-.F~*^' '`'*~*eae/: . -__/* '`_* )_. ic,_ ./- T\a 7F*-~~*a, /` dL \_,\F^ '\` .*` .,___\____._/*^* .m~ ` ' :*r(, . ~e ` -\r._____/`L @e _-**^)~*' ]c .^_ -~ ` .)L_, _-`' .]F_.,, ,.-e_@, -*#^ *~*v- '-/-~* '`]- d@,,..(, ^'*m-' i*^^` '^`

— — -- —

-v/^'vm- .__,., . -@b%, .r**#rbe-C_ .., -* bFme_F` %)b)) -dF` '^'* '#b@_ia*_, , ._ -*e)'*b@@(, i_Lm]F .m@F`7%, *L.,^` -~%@(md-` . ..F.- -/bc.d@)Fm/Lde dL/ab@* _,_ 'Tbdb -*.d@e __@F7_ -7** i__ ` ._TFF@br@Ce/bebC- _md@* ae___. ., ^^_-**@F@%F7F^._,, -@F._a_mmdd@m@d@ *\m)bb/*@@@L(*@@_m/`^ ^*-```@)#F(@@#^v_%%%@#@*@@(m_r,^*** - -*\.m@@*#@dF@d@F T@d@F , .rve_ `.a, ._ a_d@(C@- ` ' -a@F%F.*L,.d ^` ,^mea_ *@r*FT@**` *T@L:md@C7_ )bd@@@c. _.d@C '*#m@@@C* m@*^@@Lbm_^^7@c .m/FFT*^ ,._v, `` -***^@)\mL*@c ,@d@@`^ iF^^** ''^~**#e, .._@@*^.__ ^'@m._ '` .___r/F7`-r./@e, ae_%T@mb_ , '^'^^`^^`^^^^`'`^^^^^^^` `

— — -- —

i-/`:bc.. .--/:-- -\,\_*^ ^ .dbmL/ '^^]/^` ,._**%^` c /r^#_ _ .a(bd *-@/%, , . d/mC_ _L, i_e/`'- )c #e@_- '-*^ec., ^Ta _-e-**` v,. ._, -:F-a,i_, --\F-- 'b~^' , _ '*i/-*` -^ -*/%,._ ''~`*mc i i,'@) _, ,. *eC-*^~/*- ~ */d., _,'@,#[][]Faa*._ '*/L**`b~* ` **C .v/^vd*:`]L'a*`a*`./)F](*- .,_ ,. ..._d-m\__F*e*bd@@@@\d*a**:_,, . -\F-r((--*F^ .LL%%%)d@*''@b@@77%%dL , i_.,].c '`@- ''` _L__/')@@bmmd@@bdd_L,,. _\_\\-(\:*7T: ., _._a-^a**F@F*F*\/-e_`^*^(:` ' _ -(b/**^.r*\a^b'F][*_^\.^* '\@ _ ., '-de-*^/T, 'ir*.d*][ b ^v. '@\_._- '-:b_*^`*\- ` -#- ` * *#.r-- `:F\.F,._c _m/*@*_ ._am~v_ -*@*F^ ' 'Tm)- e_ ^ -_mr*^ db-- `_^\/-` '^]'` '* ._-.*``` ''c__ ^@/v% . , _, _-*^- -~F- .'*a-F` -.@/L, -.d@av, '\m*m: ,. '^' ^` ^^`^` ^` ^^

— — -- —

-1.999 985 881 278 +0.000 000 000 001 i @ .000 000 000 300 -, \ '-, \ , . \ , [ ` , \ ~ ` ] ^--.. '- ', \ - . ' , '^--,_ '`, '- \ .',i',,[,/ `--.. -, -, `,-,~,\'\/b@mai` `^-._ `-, ~,*'\'\(d))d@F*@@[ `--_ '-,~/\~._\_/@F**` ^*` ---__,:-`v//(@@@#@@* _____________________________~.Ldbb@@*` '* __.***F#T#@@,,__e ^`` ,.-:-\--/@F@@*@e, . .,-^` ,--',\~~\.((@b@mc:md[ ..,--' ..- /~ '/`/`)~*\(@@d@)[ _,,-^' ' .,- .- .*-~/`~/F^`,- .._--^` ., .' i~ . '. ``', --^' .,' ' a` i` ' i _- .` / c ' .-` .` [ ., .` '' `

— — -- —

Use smaller grid because I'm doing development on PowerBook {This was a PowerBook 140, a model which had no hardware floating-point capability}. Replace most "*" with '"'; one ":" case becomes ";"

-, ._)/, ._.-" '-_.. :_ ,, :r` `\_ ,a)~^~\/ ]` -----*(%, . -: `:)/_/~\ 'c ' ` '",_ _,/^ '^'7r.:F^'' ^)\` ^`

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

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2022 Mar 28.

s.27