I decided to make a page cataloging odd ways of generating Mandelbrot Sets, abusing various programming languages along the way. I can’t take any credit for coming up with these and I’ve tried to list the credit as far as I know where it is.
T-SQL
An ASCII rendition can be happily produced by MSSQL by executing the following query:
-- AUTHOR: GRAEME JOB -- CREATED: 12-OCT-2008 -- BECAUSE: SINGLE SQL COMMAND <
50 LINES. JUST BECAUSE. WITH XGEN(X, IX) AS ( -- X DIM GENERATOR SELECT
CAST(-2.2 AS FLOAT) AS X, 0 AS IX UNION ALL SELECT CAST(X + 0.031 AS FLOAT) AS
X, IX + 1 AS IX FROM XGEN WHERE IX < 100 ), YGEN(Y, IY) AS ( -- Y DIM
GENERATOR SELECT CAST(-1.5 AS FLOAT) AS Y, 0 AS IY UNION ALL SELECT CAST(Y +
0.031 AS FLOAT) AS Y, IY + 1 AS IY FROM YGEN WHERE IY < 100 ), Z(IX, IY, CX,
CY, X, Y, I) AS ( -- Z POINT ITERATOR SELECT IX, IY, X, Y, X, Y, 0 FROM XGEN,
YGEN UNION ALL SELECT IX, IY, CX, CY, X * X - Y * Y + CX AS X, Y * X * 2 + CY,
I + 1 FROM Z WHERE X * X + Y * Y < 16 AND I < 100 ) SELECT REPLACE(REPLACE(REP
LACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE( REPLACE(REPLACE(
REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(
REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(
(X0+X1+X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14+X15+X16+X17+X18+X19+ X20+X2
1+X22+X23+X24+X25+X26+X27+X28+X29+X30+X31+X32+X33+X34+X35+X36+X37+X38+X39+ X40
+X41+X42+X43+X44+X45+X46+X47+X48+X49+X50+X51+X52+X53+X54+X55+X56+X57+X58+X59+
X60+X61+X62+X63+X64+X65+X66+X67+X68+X69+X70+X71+X72+X73+X74+X75+X76+X77+X78+X7
9+ X80+X81+X82+X83+X84+X85+X86+X87+X88+X89+X90+X91+X92+X93+X94+X95+X96+X97+X98
+X99), 'A',' '), 'B','.'), 'C',','), 'D',','), 'E',','), 'F','-'), 'G','-'),
'H','-'), 'I','-'), 'J','-'), 'K','+'), 'L','+'), 'M','+'), 'N','+'),
'O','%'), 'P','%'), 'Q','%'), 'R','%'), 'S','@'), 'T','@'), 'U','@'),
'V','@'), 'W','#'), 'X','#'), 'Y','#'), 'Z',' ') FROM ( SELECT 'X' + CAST(IX
AS VARCHAR) AS IX, IY, SUBSTRING('ABCDEFGHIJKLMNOPQRSTUVWXYZ',
ISNULL(NULLIF(I, 0), 1), 1) AS I FROM Z) ZT PIVOT ( MAX(I) FOR IX IN (
X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19, X20,X21
,X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38,X39, X40,
X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51,X52,X53,X54,X55,X56,X57,X58,X59, X
60,X61,X62,X63,X64,X65,X66,X67,X68,X69,X70,X71,X72,X73,X74,X75,X76,X77,X78,X79
, X80,X81,X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98,
X99) ) AS PZT
Postscript
Printer languages are useful, but surprisingly powerful. Stick this in a file and send it to any postscript printer:
%!PS-Adobe-2.0 51 .5 551 { /x exch def 111 .5 721 { /y exch def y 521 sub 201
div x 301 sub 201 div 1 index 1 index 31 -1 1 { /n exch def 1 index dup mul 1
index dup mul 1 index 1 index add /d exch def sub 4 index add 3 1 roll 2 mul
mul 2 index add d 4 gt {exit} if } for pop pop pop pop n 31 div setgray x y
moveto .5 0 rlineto 0 .5 rlineto -.5 0 rlineto fill } for } for showpage