# A Series of Snowflakes

Published on 6 December 2012

## Subverted snowflakes or delicate doilies?

Or maybe just a patchwork of patterns...

### Related posts

- Introducing Frax
- The project I've been working on for the last two years...
- L'Eclaireur
- A series of looping animations from an installation at L'Eclaireur in Paris.
- Music Box
- A journey into a FabergĂ© inspired world.
- Fractal Lab
- A WebGL fractal explorer
- More blog posts

Randycommented at 7 December 2012 at 01:15It looks like a Mandelbrot Set.

Kai Krausecommented at 7 December 2012 at 21:53Those 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. Pagecommented at 8 December 2012 at 04:38Beautiful work Tom!

Dan Griescommented at 9 December 2012 at 01:14Beautiful and stunning!!!

micshaccommented at 10 December 2012 at 16:25Lovely

Kamrancommented at 13 December 2012 at 16:01wow, simply beautiful work!

Knightycommented at 30 December 2012 at 12:08Beautiful!

Is it a julia set and foldings mix?

Tomcommented at 30 December 2012 at 17:18They are all julia-style sets at various powers with an abs() term to effectively fold:

z' = abs(a * z^p) * b + cwhere 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.

knightycommented at 30 December 2012 at 19:19Thank you.

Frederik Vanhouttecommented at 5 February 2013 at 22:28Thanks, Tom! You just gave me the perfect material for my FMX13 talk "The fallacy of the snowflake".

Cheers!

F.

Red Rose Photoscommented at 3 March 2013 at 16:45Realy enthralling and captivating images. I spent a good half an hour looking through them individually and found them totally encapsulating.

Thanks

William Hustoncommented at 31 August 2013 at 21:38Stunning 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!