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In mathematics, an apollonian gasket, apollonian net, or apollonian circle packing is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is impossible therefore in its case to substitute the similarity dimension for the fractal dimension. In 3d one starts with 4 spheres each at the vertices of a tetrahedron
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A outer soddy sphere is added that encloses the 4 spheres It is named after the greek mathematician apollonius of perga. The gaps are filled by subsequent soddy spheres thus forming a solid object (at infinity)
The result is often called an apollonian sphere packing.
Ancillary figure for van roomen's solution to the problem of apollonius Apollonian gasket can be made using these algorithms The apollonian fractal is named after apollonius of perga (ca The apollonian gasket can also be generalized to three dimensions (boyd 1973, andrade et al
Repeating the procedure of making new circles, that are tangent to three other circles, will produce a circle fractal called an apollonian gasket When making a geometrical construction of an apollonian gasket, new circles are created from triplets of circles by using circle inversion. An apollonian gasket fractal is generated by starting with a triple of mutually tangent circles, and successively filling in more circles, each tangent to another three. Apollonian gasket an apollonian gasket is a group of three circles in which each circle is tangent to the other two
