Category : C Source Code
Archive   : FRASRC18.ZIP
Filename : FRACTINT.L

Koch1 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 6
Axiom F--F--F
F=F+F--F+F
}

Koch2 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 12
Axiom F---F---F---F
F=-F+++F---F+
}

Koch3 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 4
Axiom F-F-F-F
F=F-F+F+FF-F-F+F
}

Koch6 { ; Adrian Mariano
axiom f+f+f+f
f=f-ff+ff+f+f-f-ff+f+f-f-ff-ff+f
angle 4
}

Dragon { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 8
Axiom FX
F=
y=+FX--FY+
x=-FX++FY-
}

Peano1 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 4
Axiom F-F-F-F
F=F-F+F+F+F-F-F-F+F
}

Cesaro { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 34
Axiom FX
F=
X=----F!X!++++++++F!X!----
}

DoubleCesaro { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 4
axiom D\90D\90D\90D\90
D=\42!D!/84!D!\42
}

FlowSnake { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle=6;
axiom FL
L=FL-FR--FR+FL++FLFL+FR-",
R=+FL-FRFR--FR-FL++FL+FR",
F=
}

CantorDust { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 6
Axiom F
F=FGF
G=GGG
}

Snowflake2 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 12
axiom F
F=++!F!F--F--F@IQ3|+F!F--
F=F--F!+++@Q3F@QI3|+F!F@Q3|+F!F
}

SnowflakeColor { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 12
axiom F
F=--!F<1!F<1++F<1++F<1@IQ3|-F<1!F<1++
F=F<1++F<1!---@Q3F<1@QI3|-F<1!F<1@Q3|-F<1!F<1
<=
}

Island1 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 4
axiom F+F+F+F
F=FFFF-F+F+F-F[-GFF+F+FF+F]FF
G=@8G@I8
}

Island2 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 4
axiom f+f+f+f
f=f+gf-ff-f-ff+g+ff-gf+ff+f+ff-g-fff
g=@6G@I6
}

Quartet { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 4
axiom fb
A=FBFA+HFA+FB-FA
B=FB+FA-FB-JFBFA
F=
H=-
J=+
}

SnowFlake1 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 12
Axiom FR
R=++!FRFU++FU++FU!---@Q3FU|-@IQ3!FRFU!
U=!FRFU!|+@Q3FR@IQ3+++!FR--FR--FRFU!--
F=
}

SnowFlake3 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 12
axiom fx
x=++f!x!fy--fx--fy|+@iq3fyf!x!++f!y!++f!y!fx@q3+++f!y!fx
y=fyf!x!+++@iq3fyf!x!++f!x!++f!y!fx@q3|+fx--fy--fxf!y!++
f=
}

Tree1 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle=12;
axiom +++FX
[email protected][-FX]+FX
}

Peano2 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
Angle 8
Axiom FXY++F++FXY++F
X=XY@Q2-F@IQ2-FXY++F++FXY
Y=-@Q2F-@IQ2FXY
}

Sierpinski1 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 3
axiom F
F=FXF
X=+FXF-FXF-FXF+
}

Koch4 { ; Adrian Mariano
; from The Fractal Geometry of Nature by Mandelbrot
angle 12
axiom f++++f++++f
f=+f--f++f-
}


Plant07 { ; Ken Philip, from The Science of Fractal Images p.285b
axiom Z
z=zFX[+Z][-Z]
x=x[-FFF][+FFF]FX
angle 14
}

Plant08 { ; Ken Philip, from The Science of Fractal Images, p.286
axiom SLFFF
s=[+++Z][---Z]TS
z=+H[-Z]L
h=-Z[+H]L
t=TL
l=[-FFF][+FFF]F
angle 20
}

Hilbert { ; Ken Philip, from The Science of Fractal Images
axiom x
x=-YF+XFX+FY-
y=+XF-YFY-FX+
angle 4
}

Sierpinski3 { ; From Jim Hanan via Corbit
axiom F-F-F
f=F[-F]F
angle 3
}


Peano3 {
axiom x
x=XFYFX+F+YFXFY-F-XFYFX
y=YFXFY-F-XFYFX+F+YFXFY
angle 4
}

Koch5 {
axiom f+F+F+F
f=F+F-F-FFF+F+F-F
angle 4
}

Sierpinski2 { ; from The Science of Fractal Images
axiom FXF--FF--FF
f=FF
x=--FXF++FXF++FXF--
angle 6
}

SierpinskiSquare {
axiom F+F+F+F
f=FF+F+F+F+FF
angle 4
}


Pentagram { ; created by Adrian Mariano
angle 10
axiom fx++fx++fx++fx++fx
; f=f[[email protected]]
x=[[email protected]@[email protected]]
}


QuadKoch { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Quadratic Koch island, Figure 1.7a p.9
angle 4
AXIOM F-F-F-F-
F=F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F
}

Fass1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; FASS curve (3x3 tiles form macrotile), Figure 1.16a p.17
axiom -l
angle 4
L=LF+RFR+FL-F-LFLFL-FRFR+
R=-LFLF+RFRFR+F+RF-LFL-FR
}

Fass2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; FASS curve (4x4 tiles form macrotile), Figure 1.16b p.17
angle 4
axiom -l
L=LFLF+RFR+FLFL-FRF-LFL-FR+F+RF-LFL-FRFRFR+
R=-LFLFLF+RFR+FL-F-LF+RFR+FLF+RFRF-LFL-FRFR
}

QuadGosper { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Quadratic Gosper curve, Figure 1.11b p.12
angle 4
axiom -Fr
l=FlFl-Fr-Fr+Fl+Fl-Fr-FrFl+Fr+FlFlFr-Fl+Fr+FlFl+Fr-FlFr-Fr-Fl+Fl+FrFr-
r=+FlFl-Fr-Fr+Fl+FlFr+Fl-FrFr-Fl-Fr+FlFrFr-Fl-FrFl+Fl+Fr-Fr-Fl+Fl+FrFr
f=
}

Plant01 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24a p.25
; also p.285a The Science of Fractal Images
angle 14
axiom f
f=F[+F]F[-F]F
}

Plant02 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24b p.25
angle 18
axiom f
f=F[+F]F[-F][F]
}

Plant03 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24c p.25
angle 16
axiom f
f=FF-[-F+F+F]+[+F-F-F]
}

Plant04 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24d p.25
angle 18
axiom x
X=F[+X]F[-X]+X
F=FF
}

Plant05 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24e p.25
angle 14
axiom x
X=f[+X][-X]FX
F=FF
}

Plant06 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24f p.25
angle 16
axiom x
X=F-[[X]+X]+F[+FX]-X
F=FF
}

Plant09 { ; Adrian Mariano
axiom y
x=X[-FFF][+FFF]FX
y=YFX[+Y][-Y]
angle 14
}

Plant10 { ; Adrian Mariano
axiom f
f=f[+ff][-ff]f[+ff][-ff]f
angle 10
}


Plant11 { ; Adrian Mariano
axiom f
f=F[+F[+F][-F]F][-F[+F][-F]F]F[+F][-F]F
angle 12
}

Curve1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; curve from figure 1.9a p.10
angle 4
axiom F-F-F-F-
f=FF-F-F-F-F-F+F
}

Curve2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
angle 4
axiom F-F-F-F-
f=FF-F+F-F-FF
}

Curve3 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; curve from figure 1.9e p.10
axiom F-F-F-F-
angle 4
F=F-FF--F-F
}

Curve4 { ; Adrian Mariano
axiom yf
x=YF+XF+Y
y=XF-YF-X
angle 6
}

Leaf1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Compound leaf with alternating branches, Figure 5.12b p.130
angle 8
axiom x
a=n
n=o
o=p
p=x
b=e
e=h
h=j
j=y
x=F[+A(4)]Fy
y=F[-B(4)]Fx
[email protected]@i1.18
}

Leaf2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Compound leaf with alternating branches, Figure 5.12a p.130
angle 8
axiom a
a=f[+x]fb
b=f[-y]fa
x=a
y=b
[email protected]@i1.36
}

Bush { ; Adrian Mariano
Angle 16
Axiom ++++F
F=FF-[-F+F+F]+[+F-F-F]
}

MyTree { ; Adrian Mariano
Angle 16
Axiom ++++F
F=FF-[XY]+[XY]
X=+FY
Y=-FX
}

ColorTriangGasket { ; Adrian Mariano
Angle 6
Axiom --X
X=++FXF++FXF++FXF>1
F=FF
}

SquareGasket { ; Adrian Mariano
Angle 4
Axiom X
X=+FXF+FXF+FXF+FXF
F=FF
}

DragonCurve { ; Adrian Mariano
Angle 4
Axiom X
X=X-YF-
Y=+FX+Y
}

Square { ; Adrian Mariano
Angle 4
Axiom F+F+F+F
F=FF+F+F+F+FF
}

KochCurve { ; Adrian Mariano
Angle 6
Axiom F
F=F+F--F+F
}


Penrose1 { ; by Herb Savage
; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
; Roger Penrose's rhombuses
Angle 10
Axiom +WF--XF---YF--ZF
W=YF++ZF----XF[-YF----WF]++
X=+YF--ZF[---WF--XF]+
Y=-WF++XF[+++YF++ZF]-
Z=--YF++++WF[+ZF++++XF]--XF
F=
}

ColorPenrose1 { ; by Herb Savage
; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
; Roger Penrose's rhombuses
; Uses color to show the edge matching rules to force nonperiodicy
Angle 10
Axiom +WC02F--XC04F---YC04F--ZC02F
W=YC04F++ZC02F----XC04F[-YC04F----WC02F]++
X=+YC04F--ZC02F[---WC02F--XC04F]+
Y=-WC02F++XC04F[+++YC04F++ZC02F]-
Z=--YC04F++++WC02F[+ZC02F++++XC04F]--XC04F
F=
}

Penrose2 { ; by Herb Savage
; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
; Roger Penrose's rhombuses
Angle 10
Axiom ++ZF----XF-YF----WF
W=YF++ZF----XF[-YF----WF]++
X=+YF--ZF[---WF--XF]+
Y=-WF++XF[+++YF++ZF]-
Z=--YF++++WF[+ZF++++XF]--XF
F=
}

Penrose3 { ; by Herb Savage
; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
; Roger Penrose's rhombuses
Angle 10
Axiom [X]++[X]++[X]++[X]++[X]
W=YF++ZF----XF[-YF----WF]++
X=+YF--ZF[---WF--XF]+
Y=-WF++XF[+++YF++ZF]-
Z=--YF++++WF[+ZF++++XF]--XF
F=
}

Penrose4 { ; by Herb Savage
; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
; Roger Penrose's rhombuses
Angle 10
Axiom [Y]++[Y]++[Y]++[Y]++[Y]
W=YF++ZF----XF[-YF----WF]++
X=+YF--ZF[---WF--XF]+
Y=-WF++XF[+++YF++ZF]-
Z=--YF++++WF[+ZF++++XF]--XF
F=
}

DoublePenrose { ; by Herb Savage
; This is Penrose3 and Penrose4 superimposed
Angle 10
Axiom [X][Y]++[X][Y]++[X][Y]++[X][Y]++[X][Y]
W=YF++ZF----XF[-YF----WF]++
X=+YF--ZF[---WF--XF]+
Y=-WF++XF[+++YF++ZF]-
Z=--YF++++WF[+ZF++++XF]--XF
F=
}

Sphinx { ; by Herb Savage
; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers"
; This is an example of a "reptile"
Angle 6
Axiom X
X=+FF-YFF+FF--FFF|X|F--YFFFYFFF|
Y=-FF+XFF-FF++FFF|Y|F++XFFFXFFF|
F=GG
G=GG
}

PentaPlexity {
; Manual construction by Roger Penrose as a prelude to his development of
; the famous Penrose tiles (the kites and darts) that tile the plane
; only non-periodically.
; Translated first to a "dragon curve" and finally to an L-system
; by Joe Saverino.
Angle 10
Axiom F++F++F++F++F
F=F++F++F|F-F++F
}

; old PentaPlexity:
; Angle 10
; Axiom F++F++F++F++Fabxjeabxykabxyelbxyeahxyeabiye
; F=
; a=Fabxjea
; b=++F--bxykab
; x=++++F----xyelbx
; y=----F++++yeahxy
; e=--F++eabiye
; h=+++++F-----hijxlh
; i=---F+++ijkyhi
; j=-F+jkleij
; k=+F-klhajk
; l=+++F---lhibkl

CircularTile { ; Adrian Mariano
axiom X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X
x=[F+F+F+F[---X-Y]+++++F++++++++F-F-F-F]
y=[F+F+F+F[---Y]+++++F++++++++F-F-F-F]
angle 24
}