Self-similarity in math & ambigrams 3/3

by | Friday, August 08, 2014

Self-similarity in geometry is the idea of repeating a similar shape (often at a different scale) over and over again. In other words, a self-similar image contains copies of itself at smaller and smaller scales, such as the image below of the word “zoom.”

zoom-scaling

Self-similarity is a rich mathematical idea and connects to other powerful concepts such as infinity, iteration, fractals, recursion and so on. As it turns out self-similarity is also a rich source of ambigrams. This is why the third article in the series Of Art & Math is devoted to Self-Similarity. This series written with my friend Gaurav Bhatnagar is published by At Right Angles (a mathematics education magazine). 

screenshot

I think this is easily the best article of the three we have written so far. It has some of the best original designs I have created. Gaurav pushed me hard mathematically, and I dare say, I met the challenge (at least part of the way). I don’t want to reveal too many of the designs in the article (links to download the article are given below) but here are a couple. Below are two different designs for the word “Infinity.”

infinity-circle-and-symbol

These two different ambigram designs for “infinity” are subtly different from each other. In both cases the word can be read even when you rotate the design around – both at the top of the circle and the bottom! Notice how in the first design the chain is created by “in” mapping to itself and “finity” mapping to itself. In contrast the second design breaks the word up differently, mapping “ity” to “in” and “fin” to itself. In addition the first design wraps around a circle – for ever and ever and the second says infinity both in words and in symbol!

The idea of infinity is captured somewhat differently in the next two images.

infinity-2 styles

The first focuses on mapping the design onto a sphere while the second is a self-similar shape that circles inwards forever. In either case the design can be interpreted in two different ways. Either being made of an infinite repetition of the word “finite” or the infinite repetition of the word “infinite” (where the shape that reads as the last “e” in the word “finite” can be read as “in” in the word “infinite” when rotated by 90 degrees).

There are lot more designs in the actual article. If you love math or ambigrams are just interested in exploring some cool ideas, go ahead click the links at the end of this post.

All in all this series seeks to reveal the hidden beauty of mathematics – and thus it is only fitting that it ends with this design for “hidden beauty.”

hiddenbeauty

You can download each of the articles in the series Of Art & Math by following the links below

  1. Introducing Ambigrams: Blog postDirect link to PDF
  2. Symmetry: Blog post | direct link to PDF
  3. Self-SimilarityDirect link to PDF

Alternatively you can download all three articles in one large(-ish) PDF by clicking here.

A few randomly selected blog posts…

On taking beautiful risks

On taking beautiful risks

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Is your head in the McClouds!

Scott McCloud is a pioneer in his field - the field of comics. (I had previously posted about him here). I just discovered (via Presentation Zen & Matt Koehler) a TED talk he had given back in 2005. It is a wonderful introduction to McCloud the man and his ideas....

Forget MMORPG, its time for MMLSG

NYTimes article titled, Storming the Campuses on the next big thing on college campuses: GoCrossCampus! This new kind of a game (and game genre) has been described as Multiplayer Locally Social Gaming and the way it is spreading, it may soon need to add "Massively" to...

21st Century Learning, one school’s ongoing story

Recently I had been invited to the Birmingham School District to speak to the administrators, teachers and broader community about their recent initiatives on 21st Century Learning. I had a wonderful visit - which I was reminded of by this article (On the Front Lines...

The pleasures of being a teacher

Yesterday, as I was watching the second presidential debate, and following various bloggers who were live-blogging the event, I took a moment to check my email. I found that I had received a note from a former student. This individual had been in my summer cohort last...

MSU Technology Showcase: The Usual Suspects

I have been invited by Patrick Dickson, Byron Brown and Jon Sticklen to offer a lowkeynote address (note emphasis on lowkey!) for MSU's Second Annual Faculty Technology Showcase (more details here). I have created a small presentation to go with my lowkeynote, slides...

The joy of learning: A reflection

The joy of learning: A reflection

What is this thing called learning? What does it mean to learn something? What makes us want to learn? Why is it fun? Why do we want to know? Even as educators, we often don't take the time to ask ourselves these foundational questions. So it is rewarding when we get...

1 Comment

  1. cool math games

    cool post

    Reply

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  1. Infinite Regress: New ambigram / visual pun – Punya Mishra's Web - […] regress.” I have created many ambigrams to represent the idea of infinity (click here for examples) but this one is different…

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