Category Archives: Mathematics

Number Systems Plotter Art

Arjan van der Meij recently got an AxiDraw and has been exploring binary and ternary numbers as a plotting subject. It has been fascinating to watch his iterations on twitter and instagram. One of his earliest posts represented eight bit binary numbers as rotated squares.

He started a plot of twelve bit binary circles, but didn’t complete it due to lack of clarity. It is not too often that you get to see this type of artistic decision making in progress– many artists only post the “keepers.”

Speaking of keepers, this one involving six bit binary crossed lines was liked well enough to be replotted on notebook cover. In a further exploration of this style, he also made a 1024 grid of ten bit binary crossed lines.

This post of eight bit binary triangles explored order as well as form with a sequenced as well as a shuffled version. Nested binary shapes, like these triangles and six bit binary hexagons seem to have provoked a jump to a slightly different plotter format: laser cutter.

Some of the forms tried in wood were binary squares, eight bit binary triangles, and the seven bit binary hexagons shown above.

The jump to wood gives rise to a form that seems a bit like a jigsaw puzzle, especially when you see the individual pieces before they’ve been arranged for display.

He explores rounded shapes his series of binary flowers, including six bit binary flowers, ten bit binary flowers, and eight bit binary flowers made of ellipses.

Moving beyond binary, ternary digits have three possible values. I found the nested ternary rectangles/squares and ternary elipses (above) to be straightforward to decipher. Another method explored includes line segments, either straight or with indents or protrusions to express the values as in these ternary squares, ternary hexagon/star/circle, and ternary triangles. Other shapes are harder to describe, like folded ternary hexagons, or ternary squares with their segments folded inwards or outwards in triangles.

It is fun to compare how different number systems can be visualized using similar structures. The eight bit binary “stick figures” are not dissimilar from these six trit ternary arcs on a sticks: bits are displayed on both halves of the figure, whereas the trits are shown inline. Similarly, this set of ternary flowers bring to mind some of the the binary flowers mentioned before but have a different character for carrying more information.

One interesting diversion from the geometric forms he pursued was the text of binary numbers plotted in sequence, creating geometric patterns in the repetition of the letters. He has continued exploring various ways of visualizing and arranging numeric representations, and I’ll look forward to his continued works. If you’ve enjoyed these tastes of what he’s doing, he also posts timelapses and short videos of the process, and is making his plots available for sale on his website.

If you liked this post and have other plotter artists you’d like us to feature, please comment below or drop us a line!

Math foods for Pi Day

There are a great many ways to celebrate Pi Day, and food is one of our favorites. While pie is obviously appropriate for Pi Day, there are so many other fun ways to explore math and science through cooking. Here are some of our food projects that can be great ways to explore math concepts on Pi Day:

Happy Pi Day!

Fractals with AxiDraw

Paul Butler wrote a tutorial on Fractal Generation with L-Systems and posted some example code with the output plotted by AxiDraw.

Fractal tree drawn by AxiDraw

The tutorial is also available as a Jupyter notebook with runnable code.

Stroboscopic patterns for Easter eggs

Jiri Zemanek from Prague sent in this fabulous video of eggs decorated using the EggBot, some with markers, and some with the Electro-Kistka.

Various patterns are generated in Matlab using mathematical equations similar to ones describing Spirograph (or harmonograph) and Phyllotaxis. The patterns are calculated in such a way that when rotated under a stroboscopic light of suitable frequency or when recorded by a camera, they start to animate. It is kind of zoetrope— early device for animation. … Eggs are rotated at a constant speed, special for each pattern, by a brushless motor. No computer graphics tricks are used in the video.

Additional information is available at their site.

Computationally Fabulous Scarves

Our friend fbz just launched a kickstarter campaign to create algorithmically generated scarves, each one provably unique.

KnitYak scarves ship with the specific code and generating key used to make the pattern on your scarf. There is something powerful about knowing the mathematics and code behind the pattern you are wearing.

She’ll be getting an industrial knitting machine for her company KnitYak to automate the process of manufacturing these individualized creations.

algorithmically generated scarf design

Evil Mad Scientist Valentines: 2015 edition

Lo Res Valentines valentines

For each of the last two years, we’ve released sets of “Download and Print” cards for Valentine’s day. The 2013 set had six equation-heavy cards, and the 2014 set was a set of six symbol-heavy cards.  This year, we’re releasing six new cards, bringing the collection up to a total of 18 cards. This year’s new cards feature love, hearts, and arrows (but no bows or cupids):

My love for you is real

For when your love is complex, but not whatsoever imaginary.

I love you more every day

For that moment when you want to express that not only is the first derivative of your love positive, but so is the second.

Our love is off the charts

(Just in case there was a danger of none of these being sufficiently cheesy.)

You make me glow

Not sure how we missed this one in last year’s set of symbols.  Alternate caption: “You light up my life.”

Solve for i

And what better way to say “I love you,” than with the gift of a math problem?

2015 Evil Mad Scientist Valentines
Lo Res Valentines

You can download the full set here, which includes all 18 designs from the three years (a 765 kB .PDF document).

As usual, print them out on (or otherwise affix to) card stock, and [some steps omitted] enjoy the resulting lifelong romance.

Update: New cards have been released! Please check out the 2019 set, which contains all 42 cards from 2013 through 2019.

Digi-Comp II replica in Terraria

YouTube user Richard Lewis built a working replica of the Digi-Comp II mechanical computer in the sandbox video game Terraria.

The replica makes extensive use of the so-called “Hoik glitch” in the game, that allows for rapid, controlled player movement, much like gravity guides the balls downward in the original.

More information about the version in Terraria is posted on the video page.