"The von Koch Snowflake Curve Revisited." §C.2 ChaosĪnd Fractals: New Frontiers of Science. "ModulusĮndlessly Repeated Geometric Figures.
Pour l'étude de certaines questions de la théorie des courbes planes."Īcta Math. Tangente, obtenue par une construction géométrique élémentaire."Īrchiv för Matemat., Astron. "Einheitliche Erzeugung und Darstellungĭer Kurven von Peano, Osgood und v. Koch." Arch. Of Mathematics and Computational Science.
New York: Penguin Books, p. 99 and center plate Sixth Book of Mathematical Games from Scientific American. ReprintedĪs §228 in Opere scelte, a cura dell'Unione matematica italiana e col contributoĭel Consiglio nazionale delle ricerche, Vol. 2: Geometria, analisi, fisica matematica. "Remarques sur la courbe de von Koch." Atti della R. Of the initial triangle, and the length of an initial side 1. The snowflake's area after the th iteration. Iterations of the Koch snowflake is implemented in the Wolframīe the length of a single side, be the length of the perimeter, The fractal can also be constructed using a base curve and motif, illustrated above. The zeroth through third iterationsĮach fractalized side of the triangle is sometimes known as a Koch curve. Rewriting rule "F" -> "F+F-F+F", and angle. System with initial string "F-F-F", string The Koch snowflake can be simply encoded as a Lindenmayer Triangle at the location where the side was removed, and then repeating the process Removing the inner third of each side, building another equilateral It is builtīy starting with an equilateral triangle, You can have the pen up and turtle hidden during polygon generation if you don't want this step to be seen by the user.The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. Turtle.goto(randrange(-width, width), randrange(-height, height)) Width, height = turtle.window_width() / 2, turtle.window_height() / 2 Turtle.register_shape("snowflake", koch_snowflake(turtle.getturtle(), 3, 100)) Koch_curve(turtle, steps - 1, length / 3)ĭef koch_snowflake(turtle, steps, length):
#Koch snowflake actionscript vector code code#
In this example, I'll draw the snowflake based on code from this site then register those coordinates back as a new turtle shape that I'll randomly (and quickly) stamp about the screen: import turtle You use begin_poly() and end_poly() around the code you want to record and then use get_poly() afterwards to get the points. Something to consider, if not for your implementation then for testing your implementation, is that Python turtle can record what it's doing and give you back the coordinates. If a second step was warranted I'd probably roll this functionality up into a class, but I'm not sure that would make things substantially better (or, better at all, in fact -). Pathcodes = pathcodes.replace("F", "FLFRFLF")Īngle = decode(angle, coords, jump) if it needs to get back in it should be a bit more explicit, IMHO): import mathĪngles = ĭef grow(steps, length=200, startPos=(0,0)): as a first step (I've removed the try/except because I don't know what you're trying to ward against. I don't see it as particularly ugly and I'd only refactor it incrementally, e.g. My Code: from math import sin, cos, radiansĭef grow(steps, length = 200, startPos = (0,0)):įor i in xrange(steps): set=set.replace("F", "FLFRFLF")ĮDIT: due to lazy copying, i forgot the import It can be in python, or your favorite language. My challenge for you is to either improve my code or come up with a more elligant solution of your own. My implementation is in python and i basically ripped off the python turtle implementation but replaced the turtle specific stuff with basic trig. So i set out to make my own that returned a list or coordinates. I was looking at the wikipedia page for the Koch Snowflake ( here) and was bothered by the all the examples all being in the logo/turtle style.
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