How to generate a Mandelbrot with T-SQL?

Question

Learning a little about T-SQL, and thought an interesting exercise would be to generate a Mandelbrot set with it.

Turns out someone already has (and recently, it appears). I'll let someone else post it as an answer, but I'm curious what optimizations can be made.

Alternately, what would you do to make the code more readable?

I'll select the most readable (yet reasonably compact) version as the accepted answer (too bad we don't have rep bounties yet!) unless someone really comes along with a great optimization.

Bonus points to those answers that teach me a little something about T-SQL.

-Adam

Answer 1

From thedailywtf.com

-- 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(REPLACE(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+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+
      X60+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),
      '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,
      X60,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

_{(source: thedailywtf.com)}

Answer 2

Create PROCEDURE dbo.mandlebrot
@left float,
@right float,
@Top float,
@Bottom float,
@Res float,
@MaxIterations Integer = 500
As
Set NoCount On

Declare @Grid Table (
    X float Not Null, 
    Y float Not Null,
    InSet Bit
   Primary Key (X, Y))

Declare @Xo float, @Yo float, @Abs float
Declare @PtX Float, @PtY Float
Declare @Iteration Integer Set @Iteration = 0
Select @Xo = @Left, @Yo = @Bottom

While @Yo <= @Top Begin
    While @Xo <= @Right Begin
        Select @PtX = @Xo, @PtY = @Yo
        While @Iteration < @MaxIterations 
            And (Square(@PtX) + Square(@PtY)) < 4.0 Begin
            Select @PtX = Square(@PtX) - Square(@PtY) + @Xo,
                   @PtY = 2* @PtX * @PtY + @Yo
            Select @Iteration, @PtX, @PtY
            Set @Iteration = @Iteration + 1
        End
        Insert @Grid(X, Y, InSet) 
        Values(@Xo, @Yo, Case 
            When @Iteration < @MaxIterations
                    Then 1 Else 0 End)
        Set @Xo = @Xo + @res
        Set @Iteration = 0
    End
    Select @Xo = @Left, 
           @Yo = @Yo + @Res
End

Select * From @Grid