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More fun with Fractals


Best Answer gavinksong, 03 August 2013 - 08:46 AM

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#1 BMAD

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Posted 31 July 2013 - 09:39 PM

Fractals is a much bigger subject in mathematics than just the chaos game i proposed to brainden recently.  There is also a version of self-similar iterated fractals based off rotation, translation, reflection.

 

This is an example of one:

 

fractal rot probl.png

 

Fractals like these are made by repeating taking a "picture of a picture of a picture sort of like looking at a mirror that is directly across of a mirror.  Essentially for each image a picture is taken and either left alone or some how modified (rotation, translation, reflection, etc.)

 

For example:

 

fractal example.png

 

 

Can you determine how the first image was created (the colorful one)?


Edited by BMAD, 31 July 2013 - 09:40 PM.

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#2 gavinksong

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Posted 01 August 2013 - 07:14 AM

Spoiler for my guess


Edited by gavinksong, 01 August 2013 - 07:19 AM.

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#3 gavinksong

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Posted 01 August 2013 - 07:42 AM

Spoiler for image


Edited by gavinksong, 01 August 2013 - 07:43 AM.

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#4 BMAD

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Posted 01 August 2013 - 11:55 AM

Spoiler for image


Excellent solution. There is an even easier (and non trivial solution. The trivial being that the image present is the initial. Can anyone find it?
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#5 gavinksong

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Posted 01 August 2013 - 01:09 PM

 

Spoiler for image


Excellent solution. There is an even easier (and non trivial solution. The trivial being that the image present is the initial. Can anyone find it?

 

Spoiler for


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#6 gavinksong

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Posted 03 August 2013 - 08:28 AM

Spoiler for overlooked something obvious


Edited by gavinksong, 03 August 2013 - 08:29 AM.

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#7 gavinksong

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Posted 03 August 2013 - 08:46 AM   Best Answer

Spoiler for image

Edited by gavinksong, 03 August 2013 - 08:49 AM.

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