STAR-SHAPED SET INVERSION FRACTALS

Sphere inversion fractals

79 UN CO RR EC Multiple methods exist to calculate and represent 3-D fractals. For example, spectacular, artistic images can be obtained using quaternion algebra [1]. In this article, I will briefly discuss three relatively simple methods to calculate fractal shapes consisting only of spheres. All these methods use iterative sphere inversions. A sphere inversion is the 3-D equivalent of a circl...

Approximate Star-Shaped Decomposition of Point Set Data

Simplification or decomposition is a common strategy to handle large geometric models, which otherwise require excessive computation to process. Star-shaped decomposition partitions a model into a set of star-shaped components. A model is star shaped if and only if there exists at least one point which can see all the points of the model. Due to this interesting property, decomposing a model in...

Cantor set fractals from solitons

We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

Star-Shaped and L-Shaped Orthogonal Drawings

An orthogonal drawing of a plane graph G is a planar drawing of G, denoted by D(G), such that each vertex of G is drawn as a point on the plane, and each edge of G is drawn as a sequence of horizontal and vertical line segments with no crossings. An orthogonal polygon P is called orthogonally convex if the intersection of any horizontal or vertical line L and P is either a single line segment o...

Convexifying star-shaped polygons