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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 256 
44 "Testing the L picture for fractal generation" }{TEXT -1 1 "\n" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 380 "     In \+
order to make fractals with iterated function systems  it is nice to h
ave a test procedure to make sure you have picked your affine maps cor
rectly (and to help you adjust them later if necessary.) The procedure
 TESTMAP below, takes a list of affine functions as its input, and the
 result is a mapping -L picture like the ones in the fractal blueprint
s from Peitgen's book." }}{PARA 0 "" 0 "" {TEXT -1 209 "     Before tr
ying to generate fractal examples you should load the subroutines in t
his file, either by hitting <enter> through the entire document, or by
 choosing Edit/Execute/Worksheet from the menu toolbar." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 234 "restart:with(plots):Digits:=4:\n#e
very time you start a new fractal save and close your\n#previous fract
als work.  Then return to this window\n#and restart;  otherwise you ar
e likely to overwhelm\n#Maple and crash!  Also, save frequently." }}
{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r
edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1143 "TESTMAP:=pr
oc(funclist)   #this procedure lets you test a list of\n              \+
     #functions in your iterated function system\n  local num,#the num
ber of functions\n        i,  #dummy index\n        F,  #current funct
ion in list\n        S,  #corners of unit square\n        L,  #corners
 of letter L\n        Sq, #unit square\n        Llet,  #letter L\n    \+
    AS, #transf of square corners\n        ASq,#transf of square\n    \+
    AL, #transf of L corners\n        ALlet,  #transf of letter L\n   \+
     Pics;  #a list of pictures\nS:=[[0,0],[0,1],[1,1] ,[1,0]];\nL:=[[
.1,.9],[.1,.65],[.2,.65],[.2,.675],[.125,.675],[.125,.9]]:\nSq:=polygo
nplot(S): #polygonplot connects the dots!\nLlet:=polygonplot(L):\n   n
um:=nops(funclist):\n   for i from 1 to num do\n     F:=funclist[i]:  \+
#select ith map\n     AS[i]:=map(F,S):\n     AL[i]:=map(F,L):\n     AS
q[i]:=polygonplot(AS[i]):\n     ALlet[i]:=polygonplot(AL[i]):\n       \+
#a plot of the transformed square and letter:\n     Pics[i]:=display(
\{ASq[i],ALlet[i]\}):\n   od:\n#finally, display the unit square and a
ll its images:\ndisplay(\{Sq, seq(Pics[i],i=1..num)\},scaling=constrai
ned,\ntitle=`fractal template`);\nend:\n\n        " }}}{PARA 0 "" 0 "
" {TEXT -1 46 "Here is the standard affine map, which encodes" }}
{EXCHG {PARA 11 "" 1 "" {XPPEDIT 18 0 "AFFINE1(matrix([[x], [y]])) = x
*matrix([[a], [b]])+y*matrix([[c], [d]])+matrix([[e], [f]]);" "6#/-%(A
FFINE1G6#-%'matrixG6#7$7#%\"xG7#%\"yG,(*&F,\"\"\"-F(6#7$7#%\"aG7#%\"bG
F1F1*&F.F1-F(6#7$7#%\"cG7#%\"dGF1F1-F(6#7$7#%\"eG7#%\"fGF1" }{TEXT -1 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "or, in the alternate matri
x representation:" }}}{EXCHG {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(AFFIN
E1G6#-%'matrixG6#7$7#%\"xG7#%\"yG,&*&-F(6#7$7$%\"aG%\"cG7$%\"bG%\"dG\"
\"\"F'F:F:-F(6#7$7#%\"eG7#%\"fGF:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 97 "AFFINE1:=proc(X,a,b,c,d,e,f)\nRETURN(evalf([a*X[1]+c*
X[2]+e,\n             b*X[1]+d*X[2]+f]));\nend:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{PARA 13 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 198 "No
w if you open a new file you can use these procedures to test a templa
te and generate a fractal.  Every time you restart you will need to re
turn to this window to re-enter the procedures you need." }}}{MARK "6 \+
0 0" 776 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 
}