Thursday, November 19, 2020

Chaotic Attractors Fall 2020

 Here are chaotic attractors created by students in Mathematics Through 3D Printing Fall 2020. 





Wednesday, November 18, 2020

Boys Surface

 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

AMS Notices Article

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 Fall 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
 
Four-fold symmetry

Sierpinsky structure







Saturday, November 14, 2020

Partial Derivatives But Not Differentiable

This object was created this year by a student from last year's Mathematics Through 3D Printing (2019). It is the graph of a function with partial derivatives in both directions but which is not differentiable. 



Thursday, November 12, 2020

Mathematics Through 3D Printing


Mathematics Through 3D Printing Fall 2020 -  Forgotten keys resulted in an outdoor class time. Lucky it was a beautiful day with a pile of newly printed objects.  

Wednesday, November 11, 2020

Mathematica Objects

These objects were made by students in Mathematics Through 3D Printing, Fall 2020. The assignment was to make something neat in order to learn to use Mathematica.