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In 3d one starts with 4 spheres each at the vertices of a tetrahedron A outer soddy sphere is added that encloses the 4 spheres 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
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 It is named after the greek mathematician apollonius of perga.
It is impossible therefore in its case to substitute the similarity dimension for the fractal dimension.
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