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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