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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "Courbe, labyrinthe de P
\351ano et variantes" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Alain Esc
ulier - Programme r\351\351crit en juillet 2011 \n" }}{PARA 0 "" 0 "" 
{TEXT -1 92 "Les transformations rotations, translations, sym\351tries
 sont traduites \340 l'aide des complexes" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 " utilitair
es" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1388 "restart:\nwith(plots
): \nC2R:=Z ->[Re(Z),Im(Z)]:\nLC2R:= proc(L) local i,tp;\n      tp:=NU
LL;\n      for i to nops(L) do\n         if type(evalf(L[1]),complex) \+
then tp:=tp,C2R(L[i]): else tp:=tp,LC2R(L[i]): fi;\n      od:\n[tp]\ne
nd:\naa:=3;\nfond:=polygonplot([[0,0],[aa,0],[aa,aa],[0,aa]],color=COL
OR(RGB,0.98,1,0.9),thickness=2):\nquadrillage:=(n) -> plot(\{seq([[0,a
a*i/3^n],[aa,aa*i/3^n]],i=0..3^(n)),\n                          seq([[
aa*i/3^n,0],[aa*i/3^n,aa]],i=0..3^(n)) \},color=black,linestyle=3,thic
kness=1):\nLtrans:=(V,Liste) -> if type(evalf(Liste[1]),complex) then \+
map( u ->expand(u+V),Liste): else map( u->Ltrans(V,u),Liste) fi:\nLmul
t:=(z,Liste) -> if type(evalf(Liste[1]),complex) then map( u ->u*z,Lis
te): else map( u->Lmult(z,u),Liste) fi:\nrenverse:=proc(L) local n,i: \+
 n:=nops(L): [seq(L[n-i+1],i=1..n)]: end:\nrenversetout:=proc(L) local
 tp,i;\n     tp:=NULL:\n     for i to nops(L) do\n      if type(evalf(
L[i]),complex) then tp:=L[i],tp: else tp:=renversetout(L[i]),tp: fi;\n
     od;\n     [tp];     \n end:\nLconjugate:= proc(L) if type(L[1],co
mplex) then map(conjugate,L) else map(Lconjugate,L): fi; end:\nfond:=p
olygonplot([[-3,-3],[3,-3],[3,3],[-3,3]],color=COLOR(RGB,0.98,1,0.9)):
\nquadrillage:=proc(n) \n     local i,pas:\n     pas:=2/3^(n-1);\n    \+
 plot([seq([[-3+i*pas,-3],[-3+i*pas,+3]],i=0..3^n),\n           seq([[
-3,-3+i*pas],[3,-3+i*pas]],i=-0..3^n)],linestyle=3,color=black):\nend:
\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has \+
been redefined\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#aaG\"\"$" }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 88 " Courbes de P\351ano et variantes : les extr\351mit\351s \+
du motif sont sur une diagonale du carr\351" }}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 12 " g\351n\351ralit\351s" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 269 "#===================================================
======================\n# ====on part du carr\351 de cot\351 centr\351
 en O\n#=== le chemin de base est donc [-2-2*I,-2,-2+2*I,2*I,0,-2*I,2-
2*I,2,2+2*I]\n#=======================================================
==================\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 820 "#=========
================au sens pr\350s ======================================
====\n#==== type Dm diagonale montante :ID=motif SXR=symOX(rot(Pi/2,ID
)) ( IDr,SXRr sens inverse) \n#==== type Dd diagonale descendante :IDR
=rot(Pi/2,motif) SX=symOX(ID) ( IDRr,SXr sens inverse)\n#==== forme de
s suites : [Dm,Dd,Dm, Dd,Dm,Dd, Dm,Dd,Dm] ==> 2^9 courbes possibles\ns
uites_possibles:=proc()  local forme,i,j,k,l,m,n,o,p,q,tp,rg: global I
D, IDr, SXr, SXR, IDR, SXRr:\n    rg:=1..2:\n    forme:=[ [ID,SXR],[SX
r,IDR],[ID,SXR], [-SXr,-IDR],[IDr,SXRr],[-SXr,-IDR], [ID,SXR],[SXr,IDR
],[ID,SXR]]:\n    [seq(seq(seq( seq(seq(seq( seq(seq(seq([forme[1,i],f
orme[2,j],forme[3,k], forme[4,l],forme[5,m],forme[6,n],\n          for
me[7,o],forme[8,p],forme[9,q]],i=rg),j=rg),k=rg),l=rg),m=rg),n=rg),o=r
g),p=rg),q=rg)]:\nend: \nLsuites:=suites_possibles():" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
-1 72 " Proc\351dures de calculs et de diff\351rents trac\351s de P
\351ano et des variantes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
1231 "Peano:= proc(n, K,suite)\n    local  i,j,liste1,base,J,sx,sxr,id
,idr,idR,idRr,sxR,sxRr,depart :\n        base:=[-2-2*I,-2,-2+2*I,2*I,0
,-2*I,2-2*I,2,2+2*I];\n    #====== formes diff\351rentes selon le depa
rt choisi ==========\n     depart:=[-K*3*(1+I),K*3*(1+I)]:     #  depa
rt:=base;   #\n    liste1:=depart:\n    for i from 2 to n do\n        \+
id:=liste1/3: idr:=renversetout(id): idR:=Lmult(I,id): idRr:=renverset
out(idR): \n        sx:= Lconjugate( id): sxr:=renversetout(sx):  sxR:
=Lmult(I,sx): sxRr:=renversetout(sxR):\n        liste1:= subs(ID=id,ID
R=idR,IDRr=idRr,IDr=idr,SX=sx,SXr=sxr,SXR=sxR,SXRr=sxRr, suite) :\n   \+
     liste1:=[seq(Ltrans(base[j],liste1[j]),j=1..nops(base))]:\n      \+
  if i>2 then liste1:=map(op,liste1): fi; # on garde le motif de base \+
seulement\n    od;\nLC2R(liste1): \nend:\nPeano_motif := proc(n,K,suit
e,coul)\n  local liste :\n  if n < 1 then print(\"Le 1er param\350tre \+
est un entier >0 \") \n  else   display(plot(Peano(n,K,suite),color=co
ul),scaling=constrained):\n  fi;\nend:\nPeano_continu := proc(n,K,suit
e,coul)\n  local liste :\n  if n < 1 then print(\"Le 1er param\350tre \+
est un entier >0 \") \n   elif n=1 then liste:=Peano(n,K,suite)   else
     liste:=map(op,Peano(n,K,suite)):     fi;\n display(plot(liste,col
or=coul)):\nend:" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 " Applications" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 596 "########## suites particuli\350res  #######
##############################################################\n#-----
 wunderlich Lsuites[171] soit choix:=[ID, IDR, ID, -IDR, IDr, -IDR, ID
, IDR, ID]: \n#----- peano Lsuites[1] soit choix:=[ID, SXr, ID, -SXr, \+
IDr, -SXr, ID, SXr, ID]:\n#----- Colonnes sym\351triques  Lsuites[512]
 soit choix:=[SXR, IDR, SXR, -IDR, SXRr, -IDR, SXR, IDR, SXR]\n#######
######################################################################
######################### \nchoix:=Lsuites[50]:\nn,K:=3, 0.1;\n\n#plot
setup(gif,plotoutput=\"j:/L[50]-0.1.gif\",plotoptions=\"width=400,heig
ht=400\"):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "display([display(P
eano_motif(n,K,choix,blue),thickness=2),   display(Peano_continu(n,K,c
hoix,red),thickness=2),\n              quadrillage(n-1),fond],axes=non
e);\nplotsetup(inline);" }{TEXT -1 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>6$%\"nG%\"KG6$\"\"$$\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 384 "#==== animation ====\nn,K:=3, 1;\nP:=20;\ngr:=displa
y([display([seq(display([display(Peano_motif(n,i*K/P,choix,blue),thick
ness=3),\n                      display(Peano_continu(n,i*K/P,choix,re
d),thickness=2)]),i=0..P)],insequence=true),\nquadrillage(n-1),fond],a
xes=none):\n#plotsetup(gif,plotoutput=\"j:/variantesPeano-ordre2.gif\"
,plotoptions=\"width=500,height=500\"):\ngr;\nplotsetup(inline);" }
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%\"nG%\"KG6$\"\"$\"
\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG\"#?" }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 " Labyrinthe de P\351ano
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1032 "labPeano := proc(n,cou
l)\n   local  i,j,liste1,base,J,sx,sxr,id,idr,idR,idRr,sxR,sxRr,depart
,suite :\n        base:=[-2-2*I,-2,-2+2*I,2*I,0,-2*I,2-2*I,2,2+2*I];\n
    #====== formes diff\351rentes selon le depart choisi ==========\n \+
   depart:=[-3-I,-3+3*I,1+3*I,1-I,1+3*I]:\n    suite:=[ID,SXr,ID,  SYr
,-ID,SYr, ID,SXr,ID]:#[ID,SX,ID,SY,SO,SY,ID,SX,ID]:     \n    liste1:=
depart:\n    for i from 2 to n do\n        id:=liste1/3: idr:=renverse
tout(id):     sx:= Lconjugate( id): sxr:=renversetout(sx): \n        l
iste1:= subs(ID=id,IDr=idr,SX=sx,SXr=sxr,SY=-sx,SYr=-sxr, suite) :\n  \+
      liste1:=[seq(Ltrans(base[j],liste1[j]),j=1..nops(base))]:\n     \+
   if i>1 then liste1:=map(op,liste1): fi; # on garde le motif de base
 seulement\n    od;\nliste1:=[[-3,-3],op(LC2R(liste1))]:\nplot(\{liste
1,-liste1\},color=coul,thickness=2):\nend:\nN,K:=2, 0.2; \nchoix:=[ID,
 SXr, ID, -SXr, IDr, -SXr, ID, SXr, ID]:\npea:=map(op,Peano(N+1,K,choi
x)):\n#display([display(plot(pea,color=red),thickness=2),labPeano(N,bl
ack),quadrillage(N-1)],scaling=constrained,axes=none);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>6$%\"NG%\"KG6$\"\"#$F(!\"\"" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 330 "\n#========animation =========
= \n\n#plotsetup(gif,plotoutput=\"j:/labyrinthePeano.gif\",plotoptions
=\"width=500,height=500\"):\ngr;\ndisplay([labPeano(N,black),\n       \+
display([plot([pea[1],pea[1]]),seq(plot(pea[1..3*i]),i=1..nops(pea)/3)
],color=red,thickness=2,insequence=true)],\n       scaling=constrained
,axes=none);\nplotsetup(inline);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 69 " motif grec : les extr\351mit\351
s du motif sont sur le m\352me  cot\351 du carr\351" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 781 "#=========================au sens pr\350s \+
==========================================\n#==== type cote bas cb :ID
=motif -SX === type cote haut ch :-ID SX\n#==== type cote Gauche cg : \+
SXR -IDR === type cote droit cd : -SXR IDR\n#==== forme des suites : [
cg,cg,cb, cb,cb,ch, cd,cd,cb ] ==> 2^9 courbes possibles\nsuitesG_poss
ibles:=proc()  local forme,i,j,k,l,m,n,o,p,q,tp,rg: global ID, IDr, SX
r, SXR, IDR, SXRr:\n    rg:=1..2:\n    forme:=[ [-IDRr,SXR],[-IDRr,SXR
],[ID,-SXr], [ID,-SXr],[ID,-SXr],[-ID,SXr], [IDRr,-SXR],[IDRr,-SXR],[I
D,-SXr]]:\n    [seq(seq(seq( seq(seq(seq( seq(seq(seq([forme[1,i],form
e[2,j],forme[3,k], forme[4,l],forme[5,m],forme[6,n],\n          forme[
7,o],forme[8,p],forme[9,q]],i=rg),j=rg),k=rg),l=rg),m=rg),n=rg),o=rg),
p=rg),q=rg)]:\nend: \nLGsuites:=suitesG_possibles():" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 1387 "#======================================
==================================\n#======= K sur [0,1], ne sert pas \+
si d\351part=base =========================\nPeanoG:= proc(n, K,suite)
    \n    local  i,j,liste1,base,J,sx,sxr,id,idr,idR,idRr,sxR,sxRr,dep
art :\n        base:=[-2-2*I,-2,-2+2*I,2*I,2+2*I,2,0,-2*I, 2-2*I];\n  \+
  #====== formes diff\351rentes selon le depart choisi ==========\n   \+
 depart:= base;  #   depart:= K*[-3-3*I,3-3*I];    #  \n    liste1:=de
part:\n    for i from 2 to n do\n        id:=liste1/3: idr:=renverseto
ut(id): idR:=Lmult(I,id): idRr:=renversetout(idR): \n        sx:= Lcon
jugate( id): sxr:=renversetout(sx):  sxR:=Lmult(I,sx): sxRr:=renverset
out(sxR):\n        liste1:= subs(ID=id,IDR=idR,IDRr=idRr,IDr=idr,SX=sx
,SXr=sxr,SXR=sxR,SXRr=sxRr, suite) :\n        liste1:=[seq(Ltrans(base
[j],liste1[j]),j=1..nops(base))]:\n        if i>2 then liste1:=map(op,
liste1): fi; # on garde le motif de base seulement\n    od;\nLC2R(list
e1): \nend:\nPeanoG_motif := proc(n,K,suite,coul)\n  local liste :\n  \+
if n < 1 then print(\"Le 1er param\350tre est un entier >0 \") \n  els
e   display(plot(PeanoG(n,K,suite),color=coul),scaling=constrained):\n
  fi;\nend:\nPeanoG_continu := proc(n,K,suite,coul)\n  local liste :\n
  if n < 1 then print(\"Le 1er param\350tre est un entier >0 \") \n   \+
elif n=1 then liste:=PeanoG(n,K,suite)   else     liste:=map(op,PeanoG
(n,K,suite)):     fi;\n display(plot(liste,color=coul)):\nend:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 246 "choix:=LGsuites[512];\nn,K:
=2,0.9;\ndisplay([display(PeanoG_motif(n,K,choix,blue),thickness=2),  \+
 \n         display(PeanoG_continu(n,K,choix,red),thickness=2),\n     \+
         quadrillage(n-1),fond],axes=none,scaling=constrained);\n#plot
setup(inline);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9" 0 }
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