Tag Archives: Tiling

Apollonian gasket as a fractal in tiled hyperbolic space

Reading the fascinating book « Indra`s Pearls », written by David Mumford, Caroline Series and David Wright, you discover that the Apollonian gasket can be created by multiple inversions at four touching circles. Three of the circles are of equal … Continue reading

Posted in Fractals, Kaleidoscopes, Tilings | Tagged , , , , | Leave a comment

Apollonian gasket as a spherical fractal with tetrahedral symmetry

Before discussing the relation between the Apollonian gasket and tilings of the sphere, I want to present briefly the spherical kaleidoscope with tetrahedral symmetry. A tetrahedron has three different kinds of points with rotational symmetry. Four equilateral triangles make up … Continue reading

Posted in Anamorphosis, Fractals, Kaleidoscopes, Tilings | Tagged , , , , , | Leave a comment

class Point

For the dualization method we need a better data structure than for the projection method. Thus I defined a new class “Point” to represent grid-points and dual-points. It is an improved version of the class “TPoint”, see “TPoint – the … Continue reading

Posted in programming | Tagged , | Leave a comment

Tilings and their duals

I briefly discussed the dualization method in “The dualization method” but you will need more details to be able to understand my computer code. You can find some interesting ideas in Wolfram MathWorld and in Oracle ThinkQuest. In part I … Continue reading

Posted in Tilings | Tagged , , , , , | Leave a comment

Iteration of rhombs: the programming code

//  this is the processing code for the iteration of rhombs //  you can reproduce my results of the earlier posts //  feel free to experiment ! // //  to run it you have first to download “processing” from processing.org … Continue reading

Posted in Tilings | Tagged , , , | 6 Comments

More results from the iteration of rhombs

Iterative methods can give many different results with only some small changes. An example is the iteration of rhombs to create a tiling with eight-fold rotational symmetry, see my post “Iteration of rhombs”. Here we can use different angles for … Continue reading

Posted in Fractals, Tilings | Tagged , , , , , | 2 Comments

Why these tilings are not periodic

Often, you can put together two periodic patterns of different length and you get a new pattern, which is periodic too. The length of the period of the joint pattern is the least common multiple of the period lengths of … Continue reading

Posted in Tilings | Tagged , , , | Leave a comment