Download or view L-system-animated.frink in plain text format
// General description:
// This code creates Lindenmayer rules via string manipulation
// It can generate many of the examples from the Wikipedia page
// discussing L-system fractals: http://en.wikipedia.org/wiki/L-system
//
// It does not support stochastic, context sensitive or parametric grammars
//
// It supports four special rules, and any number of variables in rules
// f = move forward one unit
// - = turn left one turn
// + = turn right one turn
// [ = save angle and position on a stack
// ] = restore angle and position from the stack
g = new graphics
garray = new array
win = g.show[]
for turn = 0 degrees to 90 degrees step .1 degree
{
// The turn is how far each + or - in the final rule turns to either side
//turn = 90 degrees
// This is how many times the rules get applied before we draw the result
times = 10
// This is our starting string
start = "fx"
// These are the rules we apply
rules = [["f","f"],["x","x+yf"],["y","fx-y"]]
// L-System rules pulled from Wikipedia
// Dragon
// 90 degrees, "fx", [["f","f"],["x","x+yf"],["y","fx-y"]]
// TerDragon
// 120 degrees, "f", [["f","f+f-f"]]
// Koch curve
// 90 degrees, "f", [["f","f+f-f-f+f"]]
// use "++f" as the start to flip it over
// Sierpinski Triangle
// 60 degrees, "bf", [["f","f"],["a","bf-af-b"],["b","af+bf+a"]]
// Plant
// 25 degrees, "--x", [["f","ff"],["x","f-[[x]+x]+f[+fx]-x"]]
// Hilbert space filling curve
// 90 degrees, "++a", [["f","f"],["a","-bf+afa+fb-"], ["b","+af-bfb-fa+"]]
// Peano-Gosper curve
// 60 degrees, "x", [["f","f"],["x","x+yf++yf-fx--fxfx-yf+"], ["y","-fx+yfyf++yf+fx--fx-y"]]
// Lévy C curve
// 45 degrees, "f", [["f","+f--f+"]]
// This function will apply our rule once, using string substitutions based
// on the rules we pass it
// It does this in two passes to avoid problems with pairs of mutually referencing
// rules such as in the Sierpinski Triangle
// rules@k@1 could replace toString[k] and the entire second loop could
// vanish without adversely affecting the Dragon or Koch curves.
apply_rules[rules, current] :=
{
n = current
for k = 0 to length[rules]-1
{
rep = subst[rules@k@0,toString[k],"g"]
n =~ rep
}
for k = 0 to length[rules]-1
{
rep = subst[toString[k],rules@k@1,"g"]
n =~ rep
}
return n
}
// Here we will actually apply our rules the number of times specified
current = start
for i = 0 to times - 1
{
current = apply_rules[rules, current]
// Uncomment this line to see the string that is being produced at each stage
// println[current]
}
// Go ahead and plot the image now that we've worked it out
g = new graphics
theta = -4.5 turn // This value keeps a Dragon curve from rotating
g.stroke[2]
x = 0
y = 0
stack = []
for i = 0 to length[current]-1
{
// This produces a nice sort of rainbow effect where most colors appear
g.color[abs[sin[i degrees]],abs[cos[i*2 degrees]],abs[sin[i*4 degrees]]]
cur = substrLen[current,i,1]
if cur == "-"
theta = theta - turn
if cur == "+"
theta = theta + turn
if cur == "f" or cur == "F"
{
nx = x + cos[theta]
ny = y + sin[theta]
g.line[x,y,nx,ny]
x = nx
y = ny
}
if cur == "["
stack.push[[theta,x,y]]
if cur == "]"
[theta,x,y] = stack.pop[]
}
// Draw the new frame after it's been calculated.
win.replaceGraphics[g]
garray.push[g]
//g.write["dragon.png",1024,768]
}
// Now animate the already-calculated curves.
for a=1 to 3
{
reverse[garray] // Reverses array in-place.
sleep[2 s]
// Now animate in a loop.
for g = garray
{
win.replaceGraphics[g]
sleep[1/30 s]
}
}
Download or view L-system-animated.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen, eliasen@mindspring.com