def draw_stars():
t = Turtle(center_origin=True,
show_borders_and_origin=False,
animate=False,
animation_speed=0.1)
def draw_n_star(t, star_points, triangle_side=200, line_width=1):
""" Draws star
star_points: number of star point
triangle_side: line length from point ot point
"""
n = star_points
if n % 2 == 0:
n += 1
length = triangle_side
# move to position
t.penup()
t.left(90)
t.forward(length / 2)
t.pendown()
for i in range(1, n + 1):
t.left(180 - (360 / n / 2))
t.forward(length, width=line_width)
draw_n_star(t, 30, triangle_side=400)
t.save("img/star.svg")
def draw_polygons():
t = Turtle(center_origin=True,
show_borders_and_origin=False,
animate=False,
animation_speed=0.05)
def draw_n_polygon(t, polygon_sides, triangle_side=100, line_width=1):
""" Draws polygon
polygon_sides: number of sides of the polygon
triangle_side: length from the center of polygon to the endge
"""
center_triangle_angle = 360 / polygon_sides
point_angle = (180 - center_triangle_angle) / 2
for i in range(1, polygon_sides + 1):
t.penup()
t.forward(triangle_side, width=line_width)
t.right(180 - point_angle)
half = math.sin(math.radians(
center_triangle_angle / 2)) * triangle_side
t.pendown()
t.forward(half * 2, width=line_width)
t.right(180 - point_angle)
t.penup()
t.forward(triangle_side, width=line_width)
# get to right orientation
t.angle += 180
for i in range(3, 26):
draw_n_polygon(t, i, triangle_side=20 * i, line_width=i - 2)
t.save("img/3_to_25_polygons.svg")
def tree():
""" Draws tree fractal
TODO:
- randomize number of branches, angles and lengths
"""
t = Turtle(width=800,
height=800,
center_origin=True,
show_borders_and_origin=False,
animate=True,
animation_speed=0.005)
t.set_y(-400)
length = 200
branch_angle = 20
branch_scale = 0.7
steps = 10
t.left(90) # starting position
t.forward(length, width=steps / 2)
def draw_branch(length, direction, steps):
if steps == 0:
return
if direction == "left":
t.left(branch_angle)
else:
t.right(branch_angle)
t.forward(length, width=steps / 3)
draw_branch(length * branch_scale, "left", steps - 1)
draw_branch(length * branch_scale, "right", steps - 1)
t.penup()
t.back(length, width=3)
if direction == "left":
t.right(branch_angle)
else:
t.left(branch_angle)
t.pendown()
draw_branch(length * branch_scale, "left", steps)
draw_branch(length * branch_scale, "right", steps)
t.save("img/tree_fractal_animated.svg")
def draw_sierpinski_triange():
turtle = Turtle(width=1100, height=1000, center_origin=True, show_borders_and_origin=False, animate=False, animation_speed=0.001)
axiom = "B"
rules = {"A": "B+A+B", "B": "A-B-A"}
interpretation = {"A": ("forward", 4), "B": ("forward", 4), "+": ("right", 60), "-": ("left", 60)}
depth = 8
turtle.left(180)
turtle.set_x(500)
turtle.set_y(-500)
l_system_draw(turtle, "img/sierpinski_triangle.svg", axiom, rules, interpretation, depth)
def draw_hilbert_curve():
turtle = Turtle(width=1000, height=1000, center_origin=True, show_borders_and_origin=False, animate=False, animation_speed=0.001)
axiom = "-L"
rules = {"L": "LF+RFR+FL-F-LFLFL-FRFR+", "R": "-LFLF+RFRFR+F+RF-LFL-FR"}
length = 10
interpretation = {"F": ("forward", length), "+": ("right", 90), "-": ("left", 90)}
depth = 4
turtle.left(90)
turtle.set_x(400)
turtle.set_y(-400)
l_system_draw(turtle, "img/hilbert_curve.svg", axiom, rules, interpretation, depth)
def pentagram_relative():
t = Turtle(center_origin=True,
show_borders_and_origin=False,
animate=True,
animation_speed=0.5)
def draw_polygon_pentagram_relative(t, line_width=1):
n = 5
polygon_side = 200
center_angle = 360 / n
triangle_angle = (180 - center_angle) / 2
turn_angle = 180 - triangle_angle - 90
# move to starting position
x = math.cos(math.radians(turn_angle)) * polygon_side
t.penup()
t.forward(x)
t.left(180 - turn_angle)
t.pendown()
# draw polygon
for _ in range(n):
t.forward(polygon_side, width=line_width)
t.left(2 * turn_angle)
# move to position for pentagram
t.reset_angle()
t.left(180)
# draw pentagram
pentagram_polygon_side = 2 * x
for _ in range(n):
t.forward(pentagram_polygon_side, width=line_width)
t.left(180 - center_angle / 2)
t.reset()
draw_polygon_pentagram_relative(t, 5)
t.save("img/pentagram_relative_animated.svg")
def draw_koch_snowflake():
turtle = Turtle(width=1000, height=1000, center_origin=False, show_borders_and_origin=False, animate=False, animation_speed=0.001)
axiom = "F--F--F"
rules = {"F": "F+F--F+F"}
interpretation = {"F": ("forward", 1), "+": ("right", 60), "-": ("left", 60)}
depth = 6
turtle.set_x(150)
turtle.set_y(300)
l_system_draw(turtle, "img/koch_snowflake.svg", axiom, rules, interpretation, depth)
def draw_fancy_tree_3_stochastic():
turtle = Turtle(width=800, height=1000, center_origin=True, show_borders_and_origin=False, animate=False, animation_speed=0.001)
axiom = "F"
rules = {"F": ["[+F]F[−F]", "F[+F]F", "F[-F]F"]}
length = 5
angle = [25, 30, 35]
interpretation = {"F": ("forward", length), "[": ("stack", "push"), "]": ("stack", "pop"), "+": ("right", angle), "-": ("left", angle)}
depth = 9
turtle.left(90)
turtle.set_y(-500)
l_system_draw(turtle, "img/fancy_tree_3_stochastic.svg", axiom, rules, interpretation, depth, debug=True)
def draw_fancy_tree_2():
turtle = Turtle(width=700, height=1000, center_origin=True, show_borders_and_origin=False, animate=False, animation_speed=0.001)
axiom = "F"
rules = {"F": "F[+FF]F[-FF]F"}
length = 3
angle = 25.7
interpretation = {"F": ("forward", length), "[": ("stack", "push"), "]": ("stack", "pop"), "+": ("right", angle), "-": ("left", angle)}
depth = 5
turtle.left(90)
turtle.set_y(-500)
l_system_draw(turtle, "img/fancy_tree_2.svg", axiom, rules, interpretation, depth)
def draw_basic_tree():
turtle = Turtle(width=600, height=600, center_origin=True, show_borders_and_origin=False, animate=False, animation_speed=0.001)
axiom = "A"
rules = {"A": "F[+A]-A", "F": "FF"}
length = 1
angle = 30
interpretation = {"F": ("forward", length), "[": ("stack", "push"), "]": ("stack", "pop"), "+": ("right", angle), "-": ("left", angle)}
depth = 9
turtle.left(90)
turtle.set_y(-300)
l_system_draw(turtle, "img/basic_tree.svg", axiom, rules, interpretation, depth)
def snowflake():
""" Draws snowflake fractal
TODO: is broken
"""
t = Turtle(width=1000,
height=1000,
center_origin=True,
show_borders_and_origin=False,
animate=False,
animation_speed=0.01)
n = 5
pentagon_side = 20
center_angle = 360 / n
triangle_angle = (180 - center_angle) / 2
turn_angle = 2 * (180 - triangle_angle - 90)
def draw_snowflake(t, pentagon_side):
#t.set_x(x)
#t.set_y(y)
def draw_pentagon(t, pentagon_side):
for _ in range(n):
t.left(turn_angle)
t.forward(pentagon_side)
t.back(pentagon_side)
t.left(turn_angle)
for _ in range(5):
draw_pentagon(t, pentagon_side)
print(turn_angle / 2)
MAGIC = 4.2
for i in range(1, 2 * n, 2):
draw_snowflake(t, pentagon_side)
t.left(i / 2 * turn_angle) # level to 0
t.back(MAGIC * pentagon_side, width=3)
t.reset_angle()
for i in range(1, 2 * n, 2):
draw_snowflake(t, pentagon_side)
t.left(i / 2 * turn_angle) # level to 0
t.back(MAGIC * pentagon_side, width=3)
t.reset_angle()
t.save("img/snowflake_fractal.svg")