Tag Archives: actals

Andrew Hoyer, Cameron Browne, & Sphere Inversion

Welcome to this week’s Math Munch! Fractals, origami, math art, games, and a mind-bending video are all ahead, so let’s get into it.

Andrew Hoyer

Andrew Hoyer

First up, let’s take a look at the work of Andrew Hoyer.  According to his website, he’s a “software engineer in his mid-twenties living it up in sometimes sunny San Francisco.” I came across his work when I found his beautiful and completely engaging introduction to simple fractals.  (Go on! Click. Then read, experiment and play!)

Cantor Set

A Cantor set

At the bottom of that page, Andrew links to a wonderful, long list of fractals, arranged by Hausdorff dimension, which is a way of measuring fractals as being something like 2.5 dimensions.  A line is 1 dimensional.  A plane is 2D, and you can find many fractals with dimension in between!!  Weird, right?

I was also really pleased to find Andrew’s Instagram feed, which features some of his beautiful origami creations.  Andrew’s agreed to answer your questions for an upcoming Q&A, so ask away!

Compound of 5 tetrahedra Truncated Icosahedron Cube Dodecahedron
Cameron Browne

Cameron Browne

Up next, meet Cameron Browne. He’s an accomplished researcher who designs and studies games. Take a look at the many many games Cameron has created. The rules and descriptions are there, and Cameron sent along links to playable versions of a few, which you can find by clicking the pictures below.  For the third one, you’ll need to search for “Margo” or “Spargo.” For his research, Cameron investigates the possibilities of artificial intelligence, and how a computer can be used to generate games and puzzles.

Yavalath

Yavalath
description

Margo and Spargo

Margo and Spargo
description
description

Cameron is also an artist, and he has a page full of his graphic designs.  I found Cameron through his page of Truchet curves.  I love the way his pages are full of diagrams and just enough information to start making sense of things, even if it’s not perfectly clear.  Cameron also has MANY pages of wonderful fractal-ish graphics: Impossible Fractals, Cantor Knots, Fractal Board Games, Woven Horns, Efficient Trees, and on and on…  And he has agreed to do a Q&A with us, so please, submit a question. What are you wondering?

A Cantor Knot

A Cantor Knot

A Truchet curve "Mona Lisa"

A Truchet curve “Mona Lisa”

An "impossible" fractal

An “impossible” fractal

And, as if that wasn’t enough mathy awesomeness, check out this video about turning a sphere inside out.  A bit of personal history, I actually used this video  (though it was only on VHS back then, checked out from the library) as part of the research for my independent research project during my senior year of college.  It gets pretty tricky, but if you watch it all the way through it starts to make some sense.

Have a great week.  Bon appetit!

Reflection sheet – Andrew Hoyer, Cameron Browne, & Sphere Inversion