STRANGE ATTRACTORS

source:hawaii.edu
In the study of dynamical systems, an attractor is a set of points for which a solution tends to for a wide range of initial conditions. Most of these images represent the attracting set of points for some nonlinear system of differential equations. As such, any overlap or folds that appear to bring two surfaces together is just an illusion. These surfaces never touch (otherwise violating existence and uniqueness of solutions) and form a “butter pastry” like object with many surfaces squished together in a nearly zero width object. All renderings were created using the Chaoscope program. Click on images for larger versions. You can open these attractors in Chaoscope by downloading the Chaoscope files below.
.
.
.
.
.
.
.
source:artthesciencecom
Dr. Brian Wissman is an Associate Professor of Mathematics at the University of Hawai’i. His work includes creating mathematical visualizations using the Chaoscope program; a 3D rendering software used to create a comprehensible image to explain strange attractors with mathematical sciences. The results are both scientifically informed, and aesthetically beautiful.

“In the study of dynamical systems, an attractor is a set of points for which a solution tends to for a wide range of initial conditions. Most of these images represent the attracting set of points for some nonlinear system of differential equations. As such, any overlap or folds that appear to bring two surfaces together is just an illusion. These surfaces never touch (otherwise violating existence and uniqueness of solutions) and form a “butter pastry” like object with many surfaces squished together in a nearly zero width object. ” – Brain Wissman