Apollonian circle packing software

One systematically constructs a countable family of tangent circles whose radii tend to zero. The radii of an apollonian circle packing are computed from the initial curvatures e. The university of tennessee, knoxville knoxville, tennessee 37996 865974. An apollonian circle packing is a classical construction which is made by repeatedly inscribing circles into the triangular interstices in a descartes configuration of four mutually tangent circles. From apollonian circle packings to fibonacci numbers. As for apollonian gaskets, one can recursively fill new inner. Counting problems in apollonian packings american mathematical. R 1, which consist of the orbits of the four circles in d under the action of a discrete group g ad of mobius transformations inside the conformal group mob2. A new look at apollonian circle packings request pdf. The sensual apollonian circle packing sciencedirect.

Circle circle packing selenium packing problems software testing png. Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. Apollonian coronas and a new zeta function 19 pages, arxiv. More precisely, one starts from a descartes configuration, which is a set of four mutually tangent circles with disjoint interiors, suitably defined. In this work we present vapna, a visual apol lonian packing and network analysis software tool. Ken stephenson the university of tennessee, knoxville. An apollonian circle packing is any packing of circles constructed recursively from an initial configuration of four mutually tangent circles by the procedure above. How to compute the centers of circles in the apollonian circle packing. An apollonian circle packing is one of the most of beautiful circle packings whose construction can be described in a very simple manner based on an old theorem of apollonius of perga. User meh33 uploaded this circle circle packing fractal apollonian gasket.

To form such an apollonian circle packing, one starts with three mutually. One can study an apollonian circle packing acp from many different angles. The images in this paper were produced using ipe 8 and sage mathematics software 30. Computing the centers of apollonian circle packings mathoverflow. Although there are many problems in understanding all of the individual. Apollonian circle packings mark pollicott circle packings are a particularly elegant and simple way to construct quite complicated and elaborate sets in the plane. Circle packing can be seen as the art of placing tangent circles on the. Such packings are certainly of interest in classical geometry. In the current research, using computer simulation software based on discrete element method. Computing the centers of apollonian circle packings. Circle packing fractal apollonian gasket mathematics, png. An apollonian circle packing is a classical construction which. The curvatures of the circles in integral apollonian circle packings, named for apollonius of perga 262190 bc, form an infinite. Apollonian packing characterization1 geometric characterization of apollonian packings i an apollonian packing p d is a set of circles in the riemann sphere c.