The Sierpinski triangle page to end most Sierpinski triangle pages

Re:The Sierpinski triangle page to end most Sierpinski trian... by vanderZwan on Tuesday October 08, 2013 @03:47PM (#6517365)

A few years ago, I accidentally found this way of creating a Sierpinski Gasket-like structure:

https://vimeo.com/7690310

Lines "flow" from left to right (horizontally) or bottom to top (vertically), and all lines start out white. When two lines cross, they might switch color depending on which color they come across, as follows:

* white (h) + white (v) = black (h) + black (v)

* black (h) + black (v) = black (h) + black (v)

* white (h) + black (v) = white (h) + white (v)

* black (h) + white (v) = white (h) + white (v)

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Re:The Sierpinski triangle page to end most Sierpinski trian... by simcop2387 on Tuesday October 08, 2013 @07:42PM (#6518603)

What you've got there is a truth table for the XOR bitwise operation.

    HV | O
    ---+---
    11 | 0
    00 | 0
    10 | 1
    01 | 1

You can do it very similarly with the coordinates of the pixels on the screen[1]. It's really interesting how often that shape comes out of places. Which is why I think that this page got started.

[1] http://www.stilldreamer.com/mathematics/sierpinskis_triangle...

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Re:The Sierpinski triangle page to end most Sierpinski trian... by pleion on Tuesday October 08, 2013 @08:23PM (#6518760)

I designed a system of cellular automata based around this idea of colliding lines. You can play with it at http://sciencevsmagic.net/logicgrid

The XOR Sierpinksi's triangle is at http://sciencevsmagic.net/logicgrid/#282800 but there are other ways make it too. For example XNOR makes an inverse http://sciencevsmagic.net/logicgrid/#828200

If you keep hitting random you'll find plenty of surprising analogues to Sierpinksi's.

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Re:The Sierpinski triangle page to end most Sierpinski trian... by judk on Tuesday October 08, 2013 @10:35PM (#6519129)

XOR is addition mod 2, which is the same reason you get Pascal's triangle mod 2 is sierpinski gasket.

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Re:The Sierpinski triangle page to end most Sierpinski trian... by FreeFull on Wednesday October 09, 2013 @10:38AM (#6521481)

Note that where binary operations on screen coordinates tend to produce Sierpiński's triangle, ternary operations will produce Sierpiński's carpet (I don't know what happens as you increase bases beyond that, the number of possible operations does explode).

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