Phyllotaxis pattern in Python?

What is phyllotaxis pattern?

When we go back, in our botany classes and the plant world, phyllotaxis means the arrangement of flowers, leaves or seeds on a plant stem, similar to the one found in Fibonacci spiral. Based on Fibonacci sequence, the Fibonacci spiral is a set of numbers that follows a pattern similar on pascal’s triangle. The Fibonacci sequence numbers are something like - 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. So the Fibonacci sequence number is the sum of its previous numbers.

Fibonacci spirals

We generally look for symmetry and patterns to understand the objects around us. Without realizing it our eyes are seeing the Fibonacci sequences, or in the case of a sunflower head, a Fibonacci spiral.

Solution

Sunflower spiral

Example Code

import math
import turtle

def PhyllotacticPattern( t, petalstart, angle = 137.508, size = 2, cspread = 4 ):
   """print a pattern of circles using spiral phyllotactic data"""
   # initialize position
   turtle.pen(outline=1,pencolor="black",fillcolor="orange")
   # turtle.color("orange")
   phi = angle * ( math.pi / 180.0 )
   xcenter = 0.0
   ycenter = 0.0

   # for loops iterate in this case from the first value until < 4, so
   for n in range (0,t):
      r = cspread * math.sqrt(n)
      theta = n * phi

      x = r * math.cos(theta) + xcenter
      y = r * math.sin(theta) + ycenter

      # move the turtle to that position and draw
      turtle.up()
      turtle.setpos(x,y)
      turtle.down()
      # orient the turtle correctly
      turtle.setheading(n * angle)
      if n > petalstart-1:
         #turtle.color("yellow")
         drawPetal(x,y)
      else: turtle.stamp()

def drawPetal( x, y ):
   turtle.up()
   turtle.setpos(x,y)
   turtle.down()
   turtle.begin_fill()
   #turtle.fill(True)
   turtle.pen(outline=1,pencolor="black",fillcolor="yellow")
   turtle.right(25)
   turtle.forward(100)
   turtle.left(45)
   turtle.forward(100)
   turtle.left(140)
   turtle.forward(100)
   turtle.left(45)
   turtle.forward(100)
   turtle.up()
   turtle.end_fill() # this is needed to complete the last petal

turtle.shape("turtle")
turtle.speed(0) # make the turtle go as fast as possible
PhyllotacticPattern( 200, 160, 137.508, 4, 10 )
turtle.exitonclick() # lets you x out of the window when outside of idle

Solution

With a small change in your above program, you result could be displaced something like (give custom color and alter some values):