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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Von Koch snowflake" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 105 "'d' = draw a stright line in the current direction\n'r' \+
= turn right 60 degrees\n'l' = turn left 60 degrees" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 31 "lst1 := [d];  # initial segment" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Next each stage consists of replac
ing 'd' with 'dldrrdld' in the previous stage" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 55 "lst2 := subs(d=('d','l','d','r','r','d','l','d')
,lst1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "lst3 := subs(d=(
'd','l','d','r','r','d','l','d'),lst2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "lst4 := subs(d=('d','l','d','r','r','d','l','d'),lst3
);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "lst5 :
= subs(d=('d','l','d','r','r','d','l','d'),lst4);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 139 "p computes the vertices of a polygonal line start
ing at (p0x,p0y) with sides of lenght ra and \nfollowing the sequence \+
of movements in 'lst'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 461 "p
 := proc(ra, p0x, p0y, lst)\nlocal a, n, li, px, py, ang;\n    ang := \+
0;\n    px := p0x;\n    py := p0y;\n    li := [[px, py]];\n    for n t
o 1/2*length(lst) - 3/2 do\n        a := lst[n];\n        if a = 'd' t
hen\n            px := px + ra*cos(ang);\n            py := py + ra*si
n(ang);\n            li := [op(li), [px, py]]\n        elif a = 'r' th
en ang := ang - Pi/3\n        elif a = 'l' then ang := ang + Pi/3\n   \+
     else ERROR\n        end if\n    end do;\n    li\nend;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 53 "Now we plot the different stages (don't d
isplay yet!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "p1:=plot(p(
1,0,0,lst1)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "p2:=plot(p
(1/3,1.1,0,lst2)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "p3:=p
lot(p(1/9,2.2,0,lst3)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "
p4:=plot(p(1/27,3.3,0,lst4)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "p5:=plot(p(1/81,4.4,0,lst5)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 84 "Now we group them and display them at will (the final figures m
ay need to be scaled)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "di
splay(\{p1,p2,p3\},axes=NONE);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "display(\{p4,p5\},axes=NONE);" }}}}{MARK "5 0 0" 57 }
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