draw a fractal tree in Pythonista for iOS

fractal_tree_2.py

import canvas
import math

branches_drawn = 0

def along( start, direction, fraction):
	'''return a start point fraction amount in direction'''
	newstart = ( start[0] + fraction * direction[0] * math.sin(direction[1]),
	             start[1] + fraction * direction[0] * math.cos(direction[1])  )
	return newstart

def find_branches( start, direction):
	'''return a list of pairs of start+direction values for branches of the given start+direction pair'''
	# the branch parameters. these must all at least as long as angles!
	angles = [ 90, -90 ]
	start_fraction = [ .5, .5, 1, 1]
	lengths = [ .67, .67, .67, 0 ]
	result = []
	for i in range(0, len( angles)):
		result.append( ( along( start, direction, start_fraction[i]),
		                 ( direction[0]*lengths[i], direction[1]+math.radians(angles[i]) )
		               ) 
		             )
	return result

def draw_branch( start, direction):
	length = direction[0]
	#canvas.set_stroke_color( 0, color_map(length), 0)
	#canvas.set_line_width( (1 - color_map(length)) * 3 )
	endpoint = along( start, direction, 1.0)
	
	canvas.draw_line(start[0], start[1], endpoint[0], endpoint[1] )
	global branches_drawn 
	branches_drawn += 1
	if branches_drawn % 10000 == 0:
		canvas.end_updates()
		canvas.begin_updates()

def draw_tree( start, direction):
	draw_branch( start, direction)
	branches = find_branches( start, direction)
	for branch in branches:
		draw_branch( branch[0], branch[1])
		if branch[1][0] > 5:
			draw_tree( branch[0], branch[1])

def color_map(value):
	'''return a value between 0..1 with an intersting map for colors'''
	max = 128  # max possible length of a branch
	min = 5   # min possible length of a branch
	normalized = (value - min) / max
	reverse_norm = 1 - normalized
	return math.pow( reverse_norm, 3)

w = 1000 
h = 800
canvas.set_size(w, h)
start = ( w / 2, 10)
direction = ( 600, 0 ) # length, angle in radians with 0 being 'up'
canvas.begin_updates()
draw_tree( start, direction )
canvas.end_updates()