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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > IFS - Iterated Function Systems > substitution rules for various 1- and 2D nonperiodic tilings
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Author Topic: substitution rules for various 1- and 2D nonperiodic tilings  (Read 2743 times)
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kram1032
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« on: January 11, 2014, 04:14:27 PM »
http://tilings.math.uni-bielefeld.de/substitution_rules
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #1 on: February 04, 2015, 11:54:02 PM »
Tatasz at Deviantart realized a few of them in Apophysis with stunning results
And hey found a a param pack too! http://tatasz.deviantart.com/art/Substitution-Flame-Pack-341258067 wink
« Last Edit: February 05, 2015, 05:40:29 PM by DarkBeam » Logged
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cKleinhuis
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formerly known as 'Trifox'


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« Reply #2 on: February 05, 2015, 12:22:29 AM »
super nice, thank you for pointing, is there any software available to try them out?
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #3 on: February 05, 2015, 08:43:21 AM »
Well, with Apophysis you can do it using the linear variation but you must literally calculate manually position and rotation of each tile. sad
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claude
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« Reply #4 on: February 05, 2015, 12:46:04 PM »
I used a substitution tiling from there in my (probably now bitrotten) project mandulia: http://mathr.co.uk/blog/mandulia.html

And yes, it was a nightmare calculating the required transformations - the tilings database site really should have more information on that, since it must be known (there are images after all...).  Pretty much the only thing it gives is inflation factor sad
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tatasz
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« Reply #5 on: February 05, 2015, 05:48:50 PM »
Hiya folks =)
Darkbean, thanks for poking Grin with closed eyes

For me, its fairly easy - made a few tiles in apo with up to about 70 elements (like http://tatasz.deviantart.com/art/On-rails-453228104).
Calculating the positions of each xform is easy once you practice a bit - since they form a pattern, you mostly dont need to do much math, just move them around by known amounts (since you know the side lengths and the angles) etc to position them correctly.

Can help with the calcs if anyone needs because <3 tiles
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Please check my gallery: http://tatasz.deviantart.com/
claude
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« Reply #6 on: February 05, 2015, 06:13:05 PM »
btw, substitution tilings with more than one tile substitution rule are graph-directed IFS, rather than standard IFS - this makes them more similar to L-systems.  I wrote a bit about them in the graphgrow user manual, linked from http://mathr.co.uk/blog/2007-10-03_graphgrow_svg_javascript.html
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