Advanced Turtle Graphics Creating recursive drawings. Implementing L-systems for generating plant-like structures. Using the turtle module for scientific visualizations.
Creating advanced turtle graphics involves a mix of recursive drawing techniques, L-systems for simulating plant growth, and using the turtle module for scientific visualizations. Let's break down each of these concepts with examples.
Recursive Drawings
Recursive drawings are created by defining a function that calls itself to draw complex patterns. Here's an example of a simple recursive tree:
Python Code
import turtle
def draw_tree(branch_length, t):
if branch_length > 5:
t.forward(branch_length)
t.right(20)
draw_tree(branch_length - 15, t)
t.left(40)
draw_tree(branch_length - 15, t)
t.right(20)
t.backward(branch_length)
def main():
screen = turtle.Screen()
screen.bgcolor("white")
t = turtle.Turtle()
t.color("green")
t.speed(0)
t.left(90)
t.up()
t.backward(100)
t.down()
draw_tree(100, t)
screen.mainloop()
if __name__ == "__main__":
main()
Implementing L-systems
L-systems (Lindenmayer systems) are a mathematical formalism to describe the growth of plants. Here's an example of using L-systems to generate a fractal tree:
Python Code
import turtle
def apply_rules(ch):
new_str = ""
if ch == 'F':
new_str = "FF+[+F-F-F]-[-F+F+F]"
else:
new_str = ch
return new_str
def process_string(old_str):
new_str = ""
for ch in old_str:
new_str = new_str + apply_rules(ch)
return new_str
def create_lsystem(num_iters, axiom):
start_string = axiom
end_string = ""
for _ in range(num_iters):
end_string = process_string(start_string)
start_string = end_string
return end_string
def draw_lsystem(t, instructions, angle, distance):
saved_states = []
for cmd in instructions:
if cmd == 'F':
t.forward(distance)
elif cmd == '+':
t.right(angle)
elif cmd == '-':
t.left(angle)
elif cmd == '[':
saved_states.append((t.position(), t.heading()))
elif cmd == ']':
position, heading = saved_states.pop()
t.penup()
t.goto(position)
t.setheading(heading)
t.pendown()
def main():
instructions = create_lsystem(4, "F")
print(instructions)
screen = turtle.Screen()
screen.bgcolor("white")
t = turtle.Turtle()
t.color("green")
t.speed(0)
t.left(90)
t.up()
t.backward(200)
t.down()
draw_lsystem(t, instructions, 25, 5)
screen.mainloop()
if __name__ == "__main__":
main()
Scientific Visualizations
Using the turtle module for scientific visualizations can be fun and educational. For example, we can simulate the trajectory of a projectile:
Python Code
import turtle
import math
def draw_trajectory(v, angle):
g = 9.81 # gravity
angle_rad = math.radians(angle)
t = turtle.Turtle()
t.speed(0)
t.penup()
t.goto(-200, 0)
t.pendown()
for i in range(200):
t_x = i
t_y = t_x * math.tan(angle_rad) - (g * t_x ** 2) / (2 * (v * math.cos(angle_rad)) ** 2)
t.goto(t_x - 200, t_y)
def main():
screen = turtle.Screen()
screen.bgcolor("white")
v = 50 # initial velocity
angle = 45 # launch angle
draw_trajectory(v, angle)
screen.mainloop()
if __name__ == "__main__":
main()
These examples demonstrate how you can use the turtle module to create recursive drawings, implement L-systems for plant-like structures, and generate scientific visualizations. Each example can be expanded and modified for more complex and detailed graphics.
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