Day009GeneralizedKochCurve.sagews

Author: Vincent J. Matsko
Date: 18 October 2015, Day009
Post: Creating Fractals III:  Making Your Own

# Recursive function to output the highest factor of 2 within a positive integer.
# If n is odd, we're done and return 0.
# Otherwise, add 1 to the highest power of 2 within n/2.
def highestpowerof2 (n):
    if n % 2 == 1:
        return 0
    else:
        return 1 + highestpowerof2(n / 2)

highestpowerof2(1000000)

6

# These are necessary so the appropriate Python commands are available.
#from graphics import *
import matplotlib

# angle1 and angle2 are the angles to turn.  IMPORTANT: Make sure angle2 is negative!
# n is the number of steps to draw.
# len is the length of the steps.
def drawfractal(angle1, angle2, n, len):
    # Color choices.  See the blog post for details.
    colors = ["darkorchid", "firebrick", "blue", "forestgreen"]
    # currentangle keeps track of the orientation in the plane.
    currentangle = 0
    # linsegments stores the lines we'll need to draw.
    linesegments = [line([vector((0,0)),vector((len,0))])]
    # currentpoint keeps track of the end of the path.
    currentpoint = vector((len,0))
    for i in range(n):
        # First, find the appropriate angle to turn.
        if highestpowerof2(i + 1) % 2 == 0:
            currentangle += angle1
        else:
            currentangle += angle2
        # Converting to rectangular coordinates.
        nextpt = currentpoint + vector((len*cos(currentangle*pi/180),len*sin(currentangle*pi/180)))
        # Now adding the segment to the end of the path.
        linesegments.append(line([currentpoint,nextpt], color=colors[i % 4]))
        # Resetting currentpoint to the end of the path.
        currentpoint = nextpt
    show(sum(linesegments), aspect_ratio = 1, axes = False)

drawfractal(80, -140, 832, 0.2)

drawfractal(90, -210, 128, 0.2)

drawfractal(90, -250, 512, 0.2)

# angle1 and angle2 are the angles to check.
# m is the maximum number of iterations to try.
# This algorithm was created by Matthieu Pluntz, October 2015.
# See the blog post for more details.
def checkangles(angle1, angle2, m):
    sum = angle1 - angle2
    currentangle = angle1
    done = False
    count = 1
    while (count <= m) and (not(done)):
        currentangle = (sum - 2 * currentangle) % 360
        count += 1
        if (currentangle == 180):
            print "Found it!", angle1, angle2, "Level = ", count
            done = True

checkangles(90, -210, 100)

Found it! 90 -210 Level = 4

checkangles(90, -250, 100)

Found it! 90 -250 Level = 10

checkangles(11, -169, 100)

for angle in range(-359,0):
    checkangles(90, angle, 100)

Found it! 90 -354 Level = 13 Found it! 90 -346 Level = 37 Found it! 90 -338 Level = 37 Found it! 90 -330 Level = 4 Found it! 90 -322 Level = 37 Found it! 90 -314 Level = 37 Found it! 90 -306 Level = 5 Found it! 90 -298 Level = 37 Found it! 90 -290 Level = 10 Found it! 90 -282 Level = 13 Found it! 90 -274 Level = 37 Found it! 90 -270 Level = 2 Found it! 90 -266 Level = 37 Found it! 90 -258 Level = 13 Found it! 90 -250 Level = 10 Found it! 90 -242 Level = 37 Found it! 90 -234 Level = 5 Found it! 90 -226 Level = 37 Found it! 90 -218 Level = 37 Found it! 90 -210 Level = 4 Found it! 90 -202 Level = 37 Found it! 90 -194 Level = 37 Found it! 90 -186 Level = 13 Found it! 90 -178 Level = 37 Found it! 90 -170 Level = 10 Found it! 90 -162 Level = 5 Found it! 90 -154 Level = 37 Found it! 90 -146 Level = 37 Found it! 90 -138 Level = 13 Found it! 90 -130 Level = 10 Found it! 90 -122 Level = 37 Found it! 90 -114 Level = 13 Found it! 90 -106 Level = 37 Found it! 90 -98 Level = 37 Found it! 90 -90 Level = 3 Found it! 90 -82 Level = 37 Found it! 90 -74 Level = 37 Found it! 90 -66 Level = 13 Found it! 90 -58 Level = 37 Found it! 90 -50 Level = 10 Found it! 90 -42 Level = 13 Found it! 90 -34 Level = 37 Found it! 90 -26 Level = 37 Found it! 90 -18 Level = 5 Found it! 90 -10 Level = 10 Found it! 90 -2 Level = 37

drawfractal(90, -306, 512, 0.2)