Phyllotaxis pattern experiment based on code from https://www.youtube.com/watch?v=WHAQwhr1Jto

phyllotaxis_pattern_func.py

"""
Creating a phyllotaxis pattern based on formula 4.1 from
http://algorithmicbotany.org/papers/abop/abop-ch4.pdf
"""

# give Python access to Blender's functionality
import bpy

# extend Python functionality to generate random numbers
import random

# extend Python's math functionality
import math


def phyllotaxis_pattern(count, angle, ico_sphere_radius, scale_fac):

    for n in range(count):
        # calculate "φ" in formula (4.1) http://algorithmicbotany.org/papers/abop/abop-ch4.pdf
        current_angle = n * angle

        # calculate "r" in formula (4.1) http://algorithmicbotany.org/papers/abop/abop-ch4.pdf
        current_radius = scale_fac * math.sqrt(n)

        # convert from Polar Coordinates (r,φ) to Cartesian Coordinates (x,y)
        x = current_radius * math.cos(current_angle)
        y = current_radius * math.sin(current_angle)

        # place ico sphere
        bpy.ops.mesh.primitive_circle_add(radius=ico_sphere_radius, location=(x, y, 0))


count = 400

ico_sphere_radius = 0.5

# "c" in formula (4.1) http://algorithmicbotany.org/papers/abop/abop-ch4.pdf
scale_fac = 1.0

# "α" angle in radians in formula (4.1) http://algorithmicbotany.org/papers/abop/abop-ch4.pdf
# angle = math.radians(random.uniform(137.0, 138.0))

# set angle to the Fibonacci angle 137.5 to get the sunflower pattern
angle = math.radians(137.5)
phyllotaxis_pattern(count, angle, ico_sphere_radius, scale_fac)

angle = math.radians(137.0)
phyllotaxis_pattern(count, angle, ico_sphere_radius, scale_fac)

angle = math.radians(138.0)
phyllotaxis_pattern(count, angle, ico_sphere_radius, scale_fac)