はじめに
L-systemで自己回避曲線(Self-avoiding curves)を描いてみます。平面充填曲線(Space-filling curves)にもなっています。下の図をクリックすると拡大図がご覧になれます。
3角形のなかま
| 図形 | 初期規則 | 角度 | 変換規則 |
|---|---|---|---|
 |
xf+f+xf+f+xf+f | 60 | x=xf+f+xf-f-f-xf-f+f+f-f+f+f-x |
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x | 60 | x=fp+fy+fp-fp-fx-fp-fy+fp+fx y=fy-fp-fx+fp+fy+fp+fp-fx-fp p=fp f= |
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x | 60 | x=fp+fp-fx-fp+fp+fy+fp+fx-fp-fy+fp-fp-fx-fp-fy+fp+fx-fp-fy+fp+fx y=fp-fp+fy+fp-fp-fx-fp-fy+fp+fx-fp+fp+fy+fp+fx-fp-fy+fp+fx-fp-fy p=fp f=
|
 |
y3-f3-w | 30 | w=+++x--F--zFx+ x=---w++F++yFw- y=+zFx--F--z+++ z=-yFw++F++y--- |
 |
x | 60 | x=ffffwwpp+fp+fw+fp+fx-fp-fx-fp-fy+fp+fx-fp-fx-fp-fy+fp+fx-fp-fy+fp+fx y=ffffwwpp-fp-fw-fp-fy+fp+fy+fp+fx-fp-fy+fp+fy+fp+fx-fp-fy+fp+fx-fp-fy w=fffffffppppwww p=fp f= |
 |
x | 60 | x=fpa+fp+fz-fp-fz-fp-fw+fp+fz y=fpa-fp-fw+fp+fw+fp+fz-fp-fw z=ffffppppbb+fp+fpb+fp+fx-fp-fx-fp-fy+fp+fx-fp-fx-fp-fy+fp+fx-fp-fy+fp+fx w=ffffppppbb-fp-fpb-fp-fy+fp+fy+fp+fx-fp-fy+fp+fy+fp+fx-fp-fy+fp+fx-fp-fy a=ffffffppppppbbb b=fffpppaa p=fp f= |
 |
x | 30 | x=fx+fp+++fy-fp-fy-fp++fp---fx---fp-fy+++fp+fx---fp---fx+fp+++fy+++fp--fp+fx y=fy-fp---fx+fp+fx+fp--fp+++fy+++fp+fx---fp-fy+++fp+++fy-fp---fx---fp++fp-fy p=fp f= |
 |
x | 30 | x=fa+fp+++fb-fp-fb-fp++fp---fa---fp-fb+++fp+fa---fp---fa+fp+++fb+++fp--fp+fa y=fb-fp---fa+fp+fa+fp--fp+++fb+++fp+fa---fp-fb+++fp+++fb-fp---fa---fp++fp-fb a=++fy-fp++fp---fx---fp-fy+++fp+fx b=--fx+fp--fp+++fy+++fp+fx---fp-fy p=fp f= |
 |
l | 30 | l=l--f--r++f++l+f+r-- r=++l-f-r--f--l++f++r |
 |
l | 30 | l=l--f--r+f+r+f+l++f++r-f-r---f---r++f++l+f+r-- r=++l-f-r--f--l+++f+++l+f+l--f--r-f-l-f-l++f++r |
 |
x+f+y | 45 | x=x-f-y+f+x+f+y y=x-f-y-f-x+f+y |
 |
y | 30 | l=++y--f--r++++f++r-f---fl---f-y++f++l+f+++x----f--x+f+l r=r-f-y++f++++y---f-r--f--x+f+++fr+++f+l--f----l++f++x-- y=--l++f++x----f--x+f+++fy+++f+l--f--y-f---r++++f++r-f-y x=x+f+l--f----l+++f+x++f++r-f---fx---f-y++f++++y--f--r++ |
 |
l | 30 | l=---fx++++frfx- r=+fyfl----fy+++ x=+++fl----fyfl+ y=-frfx++++fr--- |
 |
l | 30 | l=---fx+++ff+rfx- r=+yfl-ff---yf+++ x=+++fl---ff-yfl+ y=-rfx+ff+++rf--- |
 |
l | 30 | l=--fx+++faf+++l--f--xflf x=fxfl--f--x+++faf+++lf-- a=ff |
4角形のなかま
| 図形 | 初期規則 | 角度 | 変換規則 |
|---|---|---|---|
 |
l | 90 | l=-rf+lfl+fr- r=+lf-rfr-fl+ |
 |
fa | 45 | a=a-f-fa+f+fa+f+fa+f+fa-f-fa-f-fa-f-fa+f+fa |
 |
faf | 45 | a=af-f-faf+f+faf+f+faf+f+faf-f-faf-f-faf-f-faf+f+fa |
 |
fl | 90 | l=lflf-rf-rf+lf+lf-rf-rflf+rf+lflfrf-lf+rf+lflf+rf-lfrf-rf-lf+lf+rfrf- r=+lflf-rf-rf+lf+lfrf+lf-rfrf-lf-rf+lfrfrf-lf-rflf+lf+rf-rf-lf+lf+rfrf f= |
 |
fl | 90 | l=lf-rfr-fl+f+lflfl+frfr- r=+lflf-rfrfr-f-rf+lfl+fr |
 |
r | 90 | l=lflf-rfr-flfl+frf+lfl+fr-f-rf+lfl+frfrfr- r=+lflflf-rfr-fl+f+lf-rfr-flf-rfrf+lfl+frfr |
 |
-l-f-l-f-l-f-l-f | 45 | l=l-f-r+f+l-f-r+f+l+f+r-f-l+f+r+f+l-f-r+f+l+f+r+f+l-f-r-f-l-f-r+f+l-f-r-f-l+f+r-f-l-f-r+f+l-f-r+f+l r=r+f+l-f-r+f+l-f-r-f-l+f+r-f-l-f-r+f+l-f-r-f-l-f-r+f+l+f+r+f+l-f-r+f+l+f+r-f-l+f+r+f+l-f-r+f+l-f-r |
 |
fx+fx+fx+fx | 90 | x=xfyfx+f+yfxfy-f-xfyfx y=yfxfy-f-xfyfx+f+yfxfy |
 |
+x+f+x+f+x+f+x+f | 90 | x=x+f+x-f-x-f-x-f-x+f+x+f+x+f+x-f-x |
 |
fxf++fxf++fxf++fxf | 45 | x=+yf--fy+ y=-xf++fx- |
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+fx+f+f+f+fx+f+f+f | 45 | x=x+f-f-f-f-f+fx+f+f+f+fx+f-f-f-f-f+fx |
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XF+F+XF+F | 90 | X=XF-F+F-XF+F+XF-F+F-X |
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L--F--L--F | 45 | L=+R-F-R+ R=-L+F+L- |
6角形のなかま
| 図形 | 初期規則 | 角度 | 変換規則 |
|---|---|---|---|
 |
fl | 60 | l=fl+fr++fr-fl--flfl-fr+ r=-fl+frfr++fr+fl--fl-fr f= |
 |
fx | 30 | x=-f++f-x-f--f+y---f--f+y+f++f-x+++f++f-x-f++f-x+++f--f+y-- y=+f++f-x-f--f+y+f--f+y---f--f+y---f++f-x+++f++f-x+++f--f+y f= |
 |
fl | 60 | l=flfl+fr--fr-fl-frfr+fl++flfl-frfr--fr-fl+fr+fl++fl-fr+flfl+fr-fl++fl+fr-fl-frfr--fr-fl++fl+fr- r=+fl-fr--fr+fl++flfl+fr+fl-fr--fr+fl-frfr-fl+fr--fr-fl-fr+fl++flfl+frfr--fr-flfl+fr+fl++fl-frfr f= |
 |
L | 60 | L=LzfR--fR-f++Lf++L-f+Lf+R--y R=z++L-fR-f+R--fR--f+Lf++LfyR z=- y=+ |
 |
fl | 60 | l=flfl-frfr-fl-frfr--fr-fl++fl+fr+flfl+fr+flflfl+frfr- r=+flfl-frfrfr-fl-frfr-fl-fr--fr+fl++flfl+fr+flfl+frfr f= |
ドラゴンカーブのなかま
| 図形 | 初期規則 | 角度 | 変換規則 |
|---|---|---|---|
 |
f+fa-f | 45 | a=a+f+fb b=a-f-fb |
 |
X | 45 | X=X+F+Y Y=X-F-Y |
 |
fx+f | 60 | x=x+f+fx-f-fx |
 |
x | 60 | x=x+f+x-f-x |
 |
fx+f+fx+f+fx+f | 60 | x=x+f+fx-f-fx |
 |
fl | 60 | l=rf+lf++lf-rf--rf+lflf++lf+rf-lf+rf--rf-lf- r=+rf+lf++lf-rf+lf-rf--rfrf-lf++lf+rf--rf-lf f= |
 |
fx+f+fx+f+fx+f | 60 | x=y-f-fy+f+fy y=x+f+fx-f-fx |
 |
fl | 90 | l=frfl+fl+fr-fl- r=+rf+lf-rf-rflf f= |
 |
x+f+x+f+x+f+x+ | 45 | x=x+f+x+f+x-f-x-f-x |