Submitted by Jean Constant on
Two examples of a 23 knot portfolio available at http://www. hermay.org/jconstant/dknots/ and based on a presentation by mathematician Richard Kramer at the National Center Center for Genome Resources in Santa Fe, NM.
Submitted by Jean Constant on
The Julia set is a set of complex numbers which do not converge to any limit when a given mapping is repeatedly applied to them (Oxford). The dynamic of the proposition was examined in the context of a finite two-dimensional surface.
Submitted by Jean Constant on
A fractal or — iterated function system — is an object or quantity that displays self-similarity on all scales (Wolfram). A minimal surface is a surface that has the smallest possible area for a surface spanning the boundary of that piece.
The object of that presentation was to evaluate how two opposite concepts could fit within the boundaries of a graphic visualization.
Submitted by Jean Constant on
The Crystallographic point groups are point groups in which translational periodicity is required . There are 32 such groups.
Following is two example from a series on the 32 point groups template developed by Prof. Steve Dutch and that focus on the dynamic of the concept.
Submitted by Jean Constant on
A conformal map is an analytic function whose derivative never vanishes within the region. The purpose of this series of visualizations was to investigate a mathematical function intended for extremely complex calculation in a tow-dimensional environment and preserve its original integrity.
Submitted by Jean Constant on
Set theory is the mathematical science of the infinite. The Cantor set is particularly well-suited for experimenting with such mathematical topics as iterated-function systems, symmetry relations, complex numbers, connectedness, and topological groups. It is also a very effective graphic visualization tool.
Submitted by Jean Constant on
Two examples from a series on 16 implicit and Boy’s surface visualization created with Richard Palais’s 3D-XplorMath software. The original shapes were manipulated in various vector graphic programs and are available at: http://www. hermay.org/jconstant/boysurface/
Submitted by Jean Constant on
Exploration of Robert Dickau’s diagrams on Bell numbers.
Submitted by Jean Constant on
Archimedean solids are convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the same way about each vertex with all sides the same length (Cromwell 1997).
In this visualization, convex polyhedra and truncated icosidodecahedra were constructed according to the Hart & Kaplan method by placing regular polygons at the rotational axes of a polyhedral symmetry group.
Submitted by Jean Constant on
Crystallography is the branch of science devoted to the study of crystalline structure. It has far-reaching applications in mineralogy, chemistry, physics, mathematics, biology and materials science (iucr.org).
A crystallographic points group is a group of symmetry operations all of which leave at least one point unmoved. The following are examples of crystallographic points group symmetries taken from a series of illustrations by the author.