Here are chaotic attractors created by students in Mathematics Through 3D Printing Fall 2020.
Wednesday, November 18, 2020
This Boys surface is a demonstration piece for how to avoid orientability problems when trying to create 3D prints of non-orientable surfaces. Instead of spending a lot of time fixing your normals on your STL file, just make it a mesh -- which also allows you to see the interesting internal geometries.
Tuesday, November 17, 2020
The article Modeling Dynamical Systems for 3D Printing by Stephen K. Lucas, Evelyn Sander, and Laura Taalman by the cover of the December 2020 issue of the AMS Notices. If you've ever wanted to print your very own chaotic attractor, check this out for instructions.
Monday, November 16, 2020
Iterated function systems are formed by iterating multi-valued affine maps of the plane or three dimensional space. These are created by students from Mathematics Through 3D Printing Fall 2020.
|Iterated function systems in the plane exhibiting 5- and 6-fold symmetries|
|The initial condition has maximum height, and the subsequent iterates are shorter and shorter.|
|Iterates of the iterated function system appear like buildings in a cityscape - in fact IFS are often used for simulation of natural landscapes|
|Starting at with the bottom disk, each subsequent height is a new iterate|