def triangle_koch(d: int = 400) -> LSystem:
c = 1
p = 0.3
q = c - p
h = (p * q)**0.5
FORWARD = BranchKind(1)
tp = Branch(angle=86, length=0)
tn = Branch(angle=-86, length=0)
def forward(d: float) -> Branch:
return Branch(angle=0, length=d, kind=FORWARD)
system = LSystem([forward(d)], recommended_depth=4)
@system.add_rule(FORWARD)
def f_replace(snapshot: BranchSnapshot) -> List[Command]:
x = snapshot.branch.length
return [
forward(x * p), tp,
forward(x * h), tn, tn,
forward(x * h), tp,
forward(x * q)
]
return system
def handle_start(_: BranchSnapshot) -> List[Command]:
out = [Branch(angle=0, length=start_length, energy=start_energy)]
for _ in range(2):
out.append(
Branch(
angle=random.randint(-10, 10),
length=start_length,
energy=start_energy,
))
out[-1].kind = BRANCH
return out
def koch_island(d: int = 10) -> LSystem:
FORWARD = BranchKind(1)
f = Branch(angle=0, length=d, kind=FORWARD)
tp = Branch(angle=90, length=0)
tn = Branch(angle=-90, length=0)
system = LSystem([f, tn, f, tn, f, tn, f], recommended_depth=4)
@system.add_rule(FORWARD)
def f_replace(_: BranchSnapshot) -> List[Command]:
return [f, tn, f, tp, f, tp, f, f, tn, f, tn, f, tp, f]
return system
def handler(t: TurtleSnapshot, branch: Branch) -> List[Command]:
new_heading = interpolate_headings(
t.heading + branch.angle,
global_heading,
branch.resistance,
force,
)
angle = new_heading - t.heading
return [branch.clone(angle=angle)]
def bushy_tree(d: int = 10) -> LSystem:
FORWARD = BranchKind(1)
f = Branch(angle=0, length=d, kind=FORWARD)
tp = Branch(angle=22.5, length=0)
tn = Branch(angle=-22.5, length=0)
push = Push()
pop = Pop()
system = LSystem([f], recommended_depth=4)
@system.add_rule(FORWARD)
def f_replace(_: BranchSnapshot) -> List[Command]:
return [
f, f, tn, push, tn, f, tp, f, tp, f, pop, tp, push, tp, f, tn, f,
tn, f, pop
]
return system
def dragon_curve(d: int = 10) -> LSystem:
T1 = BranchKind(1)
T2 = BranchKind(2)
f1 = Branch(angle=0, length=d, kind=T1)
f2 = Branch(angle=0, length=d, kind=T2)
tp = Branch(angle=90, length=0)
tn = Branch(angle=-90, length=0)
system = LSystem([f1], recommended_depth=10)
@system.add_rule(T1)
def f1_replace(_: BranchSnapshot) -> List[Command]:
return [f1, tp, f2, tp]
@system.add_rule(T2)
def f2_replace(_: BranchSnapshot) -> List[Command]:
return [tn, f1, tn, f2]
return system
def flower_field(d: int = 10) -> LSystem:
FORWARD = BranchKind(1)
f = Branch(angle=0, length=d, kind=FORWARD)
tp = Branch(angle=30, length=0)
tn = Branch(angle=-30, length=0)
push = Push()
pop = Pop()
system = LSystem([f], recommended_depth=4)
@system.add_rule(FORWARD)
def f_replace(_: BranchSnapshot) -> List[Command]:
r = random.random()
if r <= 0.33:
return [f, push, tp, f, pop, f, push, tn, f, pop, f]
elif r <= 0.66:
return [f, push, tp, f, pop, f]
else:
return [f, push, tn, f, pop, f]
return system
def weed_plant(start_energy: float = 100) -> LSystem:
def energy_to_length(energy: float) -> int:
return int(round(energy / 4))
START = BranchKind(1)
BRANCH = BranchKind(2)
LEAF = BranchKind(3)
start_length = energy_to_length(start_energy)
system = LSystem(
seed=[
Branch(angle=0,
length=start_length,
resistance=1.0,
energy=start_energy,
kind=START)
],
recommended_depth=20,
)
@system.add_rule(START)
def handle_start(_: BranchSnapshot) -> List[Command]:
out = [Branch(angle=0, length=start_length, energy=start_energy)]
for _ in range(2):
out.append(
Branch(
angle=random.randint(-10, 10),
length=start_length,
energy=start_energy,
))
out[-1].kind = BRANCH
return out
@system.add_rule(BRANCH)
def handle_branch(snapshot: BranchSnapshot) -> List[Command]:
def constrain_heading(relative_angle: float) -> float:
new_global_heading = snapshot.heading + relative_angle
too_large = True
while too_large:
if new_global_heading >= 190:
new_global_heading = 190 - random.uniform(0, 10)
elif new_global_heading <= -10:
new_global_heading = -10 + random.uniform(0, 10)
else:
too_large = False
new_relative_heading = new_global_heading - snapshot.heading
return new_relative_heading
branch = snapshot.branch
energy = branch.energy
if energy <= 30:
return [branch.clone(kind=LEAF)]
if random.random() <= 0.6:
left_energy = branch.energy * random.uniform(0.85, 0.9)
right_energy = branch.energy * random.uniform(0.85, 0.9)
gap_energy = random.uniform(
0, branch.energy * random.uniform(0.85, 0.9))
# Branch into two
left = [
Push(),
Branch(
angle=constrain_heading(random.randint(-30, -20)),
length=energy_to_length(left_energy),
energy=left_energy,
kind=BRANCH,
),
Pop(),
]
right = [
Push(),
Branch(
angle=constrain_heading(random.randint(20, 30)),
length=energy_to_length(right_energy),
energy=right_energy,
kind=BRANCH,
),
Pop(),
]
gap = Branch(angle=0,
length=energy_to_length(gap_energy),
energy=gap_energy)
if random.random() <= 5:
return [branch.clone(kind=DEFAULT_KIND), *left, gap, *right]
else:
return [branch.clone(kind=DEFAULT_KIND), *right, gap, *left]
else:
# Continue straight-ish
new_energy = branch.energy * 0.95
return [
branch.clone(kind=DEFAULT_KIND),
Branch(
angle=constrain_heading(random.randint(-10, 10)),
length=energy_to_length(new_energy),
energy=new_energy,
kind=BRANCH,
),
]
@system.add_render_rule(LEAF)
def render_leaf(t: TurtleWrapper, branch: Branch) -> None:
t.shape("circle")
t.shapesize(0.2, 1.0, 0)
t.fillcolor(0.8, 1.0, 0.8)
t.left(branch.angle)
t.forward(branch.length // 2)
t.pendown()
t.stamp()
t.penup()
return system
def handle_branch(snapshot: BranchSnapshot) -> List[Command]:
def constrain_heading(relative_angle: float) -> float:
new_global_heading = snapshot.heading + relative_angle
too_large = True
while too_large:
if new_global_heading >= 190:
new_global_heading = 190 - random.uniform(0, 10)
elif new_global_heading <= -10:
new_global_heading = -10 + random.uniform(0, 10)
else:
too_large = False
new_relative_heading = new_global_heading - snapshot.heading
return new_relative_heading
branch = snapshot.branch
energy = branch.energy
if energy <= 30:
return [branch.clone(kind=LEAF)]
if random.random() <= 0.6:
left_energy = branch.energy * random.uniform(0.85, 0.9)
right_energy = branch.energy * random.uniform(0.85, 0.9)
gap_energy = random.uniform(
0, branch.energy * random.uniform(0.85, 0.9))
# Branch into two
left = [
Push(),
Branch(
angle=constrain_heading(random.randint(-30, -20)),
length=energy_to_length(left_energy),
energy=left_energy,
kind=BRANCH,
),
Pop(),
]
right = [
Push(),
Branch(
angle=constrain_heading(random.randint(20, 30)),
length=energy_to_length(right_energy),
energy=right_energy,
kind=BRANCH,
),
Pop(),
]
gap = Branch(angle=0,
length=energy_to_length(gap_energy),
energy=gap_energy)
if random.random() <= 5:
return [branch.clone(kind=DEFAULT_KIND), *left, gap, *right]
else:
return [branch.clone(kind=DEFAULT_KIND), *right, gap, *left]
else:
# Continue straight-ish
new_energy = branch.energy * 0.95
return [
branch.clone(kind=DEFAULT_KIND),
Branch(
angle=constrain_heading(random.randint(-10, 10)),
length=energy_to_length(new_energy),
energy=new_energy,
kind=BRANCH,
),
]
def forward(d: float) -> Branch:
return Branch(angle=0, length=d, kind=FORWARD)