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Author Topic: Apollonian gasket  (Read 391 times)
GeoffW1
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« on: October 08, 2017, 08:28:30 am »

Hi,

Here's a work-in-progress, an Apollonian Gasket. I don't know why it's called a gasket, as it is nothing to do with machinery. It's a fractal, an endless repetition of a shape on an ever decreasing scale.

You can see how it goes. The 3 largest inner circles don't have to be the same dia. to start with, there are endless variations:

https://en.wikipedia.org/wiki/Apollonian_gasket

I constructed this one only by eye, using CamBam's circle properties to make small adjustments, and using Copy, Paste and Move. There are many circles yet to go, so I'll post updates. I did not directly use the maths properties of it yet, but I'm constructing an Excel spreadsheet in an effort to enter the perfect next level diameters. Wish me luck!

I figured that if I carefully constructed the 3 largest inner circles to be the same diameter to begin, then all corresponding circles around the fractal would be the same dia. as well. But they aren't!! At "level 4" I'm already having to make 1% adjustments to diameters. I think that is due to errors in fitting tangency by eye.

Anyone know of plugins or procedures I can better use?

Cheers

* Apollonian gasket.cb (9.2 KB - downloaded 14 times.)
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EddyCurrent
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« Reply #1 on: October 08, 2017, 11:34:17 am »

Some of these might be of interest;

http://www.atelier-des-fougeres.fr/Cambam/Aide/Plugins/ShapesPlugin.html
http://www.cambam.co.uk/forum/index.php?topic=4880.msg36998#msg36998
http://www.atelier-des-fougeres.fr/Cambam/Aide/Plugins/SquirclePlugin.html
http://www.atelier-des-fougeres.fr/Cambam/Aide/Plugins/VoronoiGenerator.html
http://www.atelier-des-fougeres.fr/Cambam/Aide/Plugins/TextureBuilder.html
http://www.atelier-des-fougeres.fr/Cambam/Aide/Plugins/Polygons.html
http://www.atelier-des-fougeres.fr/Cambam/Aide/Plugins/Hypocycloidal_generator.html
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EddyCurrent
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« Reply #2 on: October 09, 2017, 18:01:59 pm »

I found some code on the net so modified it very slightly for CamBam, Plugin attached below.

Warning, once it starts you have to wait until it's finished so don't go extreme on the numbers.  Wink
It will say "Finished !" in the bottom message window when done.

Once installed it appears in Plugins->Apollonian Gasket

Set the number of levels and the approximate diameter then press 'Draw'

* AppolonianGasket.zip (5.77 KB - downloaded 11 times.)

* apollo.jpg (130.37 KB, 800x700 - viewed 31 times.)
« Last Edit: October 09, 2017, 18:37:09 pm by EddyCurrent » Logged
GeoffW1
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« Reply #3 on: October 12, 2017, 03:29:09 am »

Well done Eddy
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