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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 707 "    The following, somewh
at lengthly program, is a Van Koch line fractal genorater.  What it do
es is start with a line.  The line is devided into 3 parts and the mid
dle section is either shifted up, down, to the right, or left.  There \+
is a function for each of the shift directions which are basicaly all \+
a copy of each other except for the direction which it is shifted in. \+
 The new generated line is placed in a list of lines to shifted into a
 new direction specified by the list it is placed in.  The code is far
 from an acceptable size but it does work and since speed is not a big
 issue, I don't worry about it.  The up side of this program is that i
t is relativly easy to see the individual functions." }}{PARA 0 "" 0 "
" {TEXT -1 362 "     If you wish to read this program, only read one o
f the shift functions, the other 3 are almost identical.  In fact, I c
opied them and only changed what was different.  The last function is \+
the one you call to make the fractal.  That one should be read too.  I
t basicaly calls each shift function, then takes the return from them \+
and remakes the shift lists." }}{PARA 0 "" 0 "" {TEXT -1 249 "   There
 is one error in this code.  In the main function, the loop doesn't wo
rk properly.  To repeat the loop 4 times, a value of around 30 must be
 put in.  Otherwise, it does work.  If you see the problem, please con
tact me at jawney@hotmail.com  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 142 "   An more detailed explanation of the V
an Koch line fractal can be seen on the web at: http://pages.infinit.n
et/garrick/fractals/vankoch.html" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 839 "hzlnup:=proc(hzlist)\nlocal i,lne,lf_pt,rt_pt,space,
mlf_pt,mlf_pt_up,mrt_pt,mrt_pt_up, hzlist2up,vtlist2lf,vtlist2rt;\nfor
 i to nops(hzlist) do\nlne:=op(i,hzlist);\nlf_pt:=op(1,lne);\nrt_pt:=o
p(2,lne);\nspace:=abs(rt_pt[1]-lf_pt[1])/3;\nmlf_pt:=[ lf_pt[1] + spac
e, lf_pt[2] ];\nmlf_pt_up:=[ lf_pt[1] + space, lf_pt[2] + space ];\nmr
t_pt:=[ lf_pt[1] + 2*space, lf_pt[2] ];\nmrt_pt_up:=[ lf_pt[1] + 2*spa
ce, lf_pt[2] + space ];\nnew_hz.i.1:=[lf_pt,mlf_pt];\nnew_hz.i.2:=[mlf
_pt_up,mrt_pt_up];\nnew_hz.i.3:=[mrt_pt,rt_pt];\nnew_vt.i.1:=[mlf_pt,m
lf_pt_up];\nnew_vt.i.2:=[mrt_pt,mrt_pt_up];\nod;\nhzlist2up:=[ \nseq(n
ew_hz.i.1,i=1..nops(hzlist)),\nseq(new_hz.i.2,i=1..nops(hzlist)),\nseq
(new_hz.i.3,i=1..nops(hzlist)) ];\nvtlist2lf:=[\nseq(new_vt.i.2,i=1..n
ops(hzlist)) ];\nvtlist2rt:=[\nseq(new_vt.i.1,i=1..nops(hzlist)) ];\nR
ETURN(hzlist2up,vtlist2lf,vtlist2rt);\nend:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 839 "vtlnrt:=proc(vtlist)\nlocal i,lne,bt_pt,tp_pt,spa
ce,mbt_pt,mbt_pt_rt,mtp_pt,mtp_pt_rt, hzlist2up,vtlist2rt,hzlist2dn;\n
for i to nops(vtlist) do\nlne:=op(i,vtlist);\nbt_pt:=op(1,lne);\ntp_pt
:=op(2,lne);\nspace:=abs(tp_pt[2]-bt_pt[2])/3;\nmbt_pt:=[ bt_pt[1], bt
_pt[2] + space ];\nmbt_pt_rt:=[ bt_pt[1] + space, bt_pt[2] + space ];
\nmtp_pt:=[ bt_pt[1], bt_pt[2] + 2*space ];\nmtp_pt_rt:=[ bt_pt[1] + s
pace, bt_pt[2] + 2*space ];\nnew_vt.i.1:=[bt_pt,mbt_pt];\nnew_vt.i.2:=
[mbt_pt_rt,mtp_pt_rt];\nnew_vt.i.3:=[mtp_pt,tp_pt];\nnew_hz.i.1:=[mbt_
pt,mbt_pt_rt];\nnew_hz.i.2:=[mtp_pt,mtp_pt_rt];\nod;\nvtlist2rt:=[ \ns
eq(new_vt.i.1,i=1..nops(vtlist)),\nseq(new_vt.i.2,i=1..nops(vtlist)),
\nseq(new_vt.i.3,i=1..nops(vtlist)) ];\nhzlist2dn:=[\nseq(new_hz.i.2,i
=1..nops(vtlist)) ];\nhzlist2up:=[\nseq(new_hz.i.1,i=1..nops(vtlist)) \+
];\nRETURN(vtlist2rt,hzlist2up,hzlist2dn);\nend:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 839 "vtlnlf:=proc(vtlist)\nlocal i,lne,bt_pt,tp_p
t,space,mbt_pt,mbt_pt_lf,mtp_pt,mtp_pt_lf, hzlist2up,vtlist2lf,hzlist2
dn;\nfor i to nops(vtlist) do\nlne:=op(i,vtlist);\nbt_pt:=op(1,lne);\n
tp_pt:=op(2,lne);\nspace:=abs(tp_pt[2]-bt_pt[2])/3;\nmbt_pt:=[ bt_pt[1
], bt_pt[2] + space ];\nmbt_pt_lf:=[ bt_pt[1] - space, bt_pt[2] + spac
e ];\nmtp_pt:=[ bt_pt[1], bt_pt[2] + 2*space ];\nmtp_pt_lf:=[ bt_pt[1]
 - space, bt_pt[2] + 2*space ];\nnew_vt.i.1:=[bt_pt,mbt_pt];\nnew_vt.i
.2:=[mbt_pt_lf,mtp_pt_lf];\nnew_vt.i.3:=[mtp_pt,tp_pt];\nnew_hz.i.1:=[
mbt_pt_lf,mbt_pt];\nnew_hz.i.2:=[mtp_pt_lf,mtp_pt];\nod;\nvtlist2lf:=[
 \nseq(new_vt.i.1,i=1..nops(vtlist)),\nseq(new_vt.i.2,i=1..nops(vtlist
)),\nseq(new_vt.i.3,i=1..nops(vtlist)) ];\nhzlist2dn:=[\nseq(new_hz.i.
2,i=1..nops(vtlist)) ];\nhzlist2up:=[\nseq(new_hz.i.1,i=1..nops(vtlist
)) ];\nRETURN(vtlist2lf,hzlist2up,hzlist2dn);\nend:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 839 "hzlndn:=proc(hzlist)\nlocal i,lne,lf_pt,
rt_pt,space,mlf_pt,mlf_pt_dn,mrt_pt,mrt_pt_dn, hzlist2dn,vtlist2lf,vtl
ist2rt;\nfor i to nops(hzlist) do\nlne:=op(i,hzlist);\nlf_pt:=op(1,lne
);\nrt_pt:=op(2,lne);\nspace:=abs(rt_pt[1]-lf_pt[1])/3;\nmlf_pt:=[ lf_
pt[1] + space, lf_pt[2] ];\nmlf_pt_dn:=[ lf_pt[1] + space, lf_pt[2] - \+
space ];\nmrt_pt:=[ lf_pt[1] + 2*space, lf_pt[2] ];\nmrt_pt_dn:=[ lf_p
t[1] + 2*space, lf_pt[2] - space ];\nnew_hz.i.1:=[lf_pt,mlf_pt];\nnew_
hz.i.2:=[mlf_pt_dn,mrt_pt_dn];\nnew_hz.i.3:=[mrt_pt,rt_pt];\nnew_vt.i.
1:=[mlf_pt_dn,mlf_pt];\nnew_vt.i.2:=[mrt_pt_dn,mrt_pt];\nod;\nhzlist2d
n:=[ \nseq(new_hz.i.1,i=1..nops(hzlist)),\nseq(new_hz.i.2,i=1..nops(hz
list)),\nseq(new_hz.i.3,i=1..nops(hzlist)) ];\nvtlist2lf:=[\nseq(new_v
t.i.2,i=1..nops(hzlist)) ];\nvtlist2rt:=[\nseq(new_vt.i.1,i=1..nops(hz
list)) ];\nRETURN(hzlist2dn,vtlist2lf,vtlist2rt);\nend:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 1166 "square_flake_fractal:=proc(timss)
\nlocal i, hzlistup,vtlistlf,hzback,vtback,p1,p2,p3,p4,hzback2,vtback2
,vtlistrt,hzlistdn;\nhzlistup:=[[[-5,5],[5,5]]];\nvtlistrt:=[[[5,-5],[
5,5]]];\nvtlistlf:=[[[-5,-5],[-5,5]]];\nhzlistdn:=[[[-5,-5],[5,-5]]];
\nfor i from 1 to timss do\nhzback:=[hzlnup(hzlistup)];\nhzback2:=[hzl
ndn(hzlistdn)];\nvtback:=[vtlnlf(vtlistlf)];\nvtback2:=[vtlnrt(vtlistr
t)];\nhzlistup:=[ \nseq(hzback[1][i],i=1..nops(hzback[1])),\nseq(vtbac
k[2][i],i=1..nops(vtback[2])),\nseq(vtback2[2][i],i=1..nops(vtback2[2]
)) ];\nhzlistdn:=[ \nseq(hzback2[1][i],i=1..nops(hzback[1])),\nseq(vtb
ack[3][i],i=1..nops(vtback[3])),\nseq(vtback2[3][i],i=1..nops(vtback2[
3])) ];\nvtlistlf:=[ \nseq(vtback[1][i],i=1..nops(vtback[1])),\nseq(hz
back[2][i],i=1..nops(hzback[2])),\nseq(hzback2[2][i],i=1..nops(hzback2
[2])) ];\nvtlistrt:=[ \nseq(vtback2[1][i],i=1..nops(vtback[1])),\nseq(
hzback[3][i],i=1..nops(hzback[3])),\nseq(hzback2[3][i],i=1..nops(hzbac
k2[3])) ];\nod;\np1:=plot(hzlistup,x=-20..20, color=red):\np2:=plot(hz
listdn,x=-20..20, color=red):\np3:=plot(vtlistlf,x=-20..20, color=red)
:\np4:=plot(vtlistrt,x=-20..20, color=red):\nplots[display]([p1,p2,p3,
p4], view=[-10..10,-10..10], axes=NONE);\nend: " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "square_flake_fractal(4);" }}{PARA 13 "" 1 "" 
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