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A Series of Snowflakes

Published on 6 December 2012

Subverted snowflakes or delicate doilies?

Or maybe just a patchwork of patterns...

Tags: Fractals, Patterns   Last updated: 6 December 2012

12 Comments

  • Randy commented at 7 December 2012 at 01:15

    It looks like a Mandelbrot Set.

  • Kai Krause commented at 7 December 2012 at 21:53

    Those are wonderful structures !

    These invoke the feeling of being 2D crosscut sections
    of utterly complex 3D objects...

    ...but actually they are indications
    that you Tom are a 3D shadow of an utterly complex 4D being ;)

    It has been great fun to get to know you
    well, a little crosscut of you, at least...

    MC Escher is smiling at this from the impossible heavens

    Cheers, Kai Krause

  • Randall C. Page commented at 8 December 2012 at 04:38

    Beautiful work Tom!

  • Dan Gries commented at 9 December 2012 at 01:14

    Beautiful and stunning!!!

  • micshac commented at 10 December 2012 at 16:25

    Lovely

  • Kamran commented at 13 December 2012 at 16:01

    wow, simply beautiful work!

  • Knighty commented at 30 December 2012 at 12:08

    Beautiful!
    Is it a julia set and foldings mix?

  • Tom commented at 30 December 2012 at 17:18

    They are all julia-style sets at various powers with an abs() term to effectively fold:
    z' = abs(a * z^p) * b + c
    where p is real but a, b, c are complex.

    I'm also using a standard accumulative exponential index for colouring:
    idx += exp(-1/abs(d))
    where d is the difference between length of the current and previous value of z.

  • knighty commented at 30 December 2012 at 19:19

    Thank you.

  • Frederik Vanhoutte commented at 5 February 2013 at 22:28

    Thanks, Tom! You just gave me the perfect material for my FMX13 talk "The fallacy of the snowflake".
    Cheers!

    F.

  • Red Rose Photos commented at 3 March 2013 at 16:45

    Realy enthralling and captivating images. I spent a good half an hour looking through them individually and found them totally encapsulating.

    Thanks

  • William Huston commented at 31 August 2013 at 21:38

    Stunning images.

    I was just thinking about a mental puzzle
    unit area vs. circumference (perimeter length)
    of various regular polygons.

    Show these polygons of unit area,
    and show the circumference:
    (or sum of length of sides)

    Circle=3.5
    Pentagon=3.8
    Square=4
    Equilateral triangle=4.5

    Then ask the student:
    Is it possible to construct a polygon
    (closed arc)
    with a unit area=1
    with a perimeter length > 4.5?

    And the answer is of course YES.
    I believe it is possible for
    one to construct a closed arc
    of unit area with a fractal boundary
    of any arbitrary length from 4.5 to infinity.

    Thanks for the pretty pictures!

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