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.

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Check this out. Very strange and a lot of fun.

On merging with our technologies (Unpacking McLuhan 4/3)

On merging with our technologies (Unpacking McLuhan 4/3)

This is the fourth of what was supposed to be a three post-series about how media influence our thinking. The first post, uses the invention of writing and print to unpack the meaning of McLuhan’s statement, “The medium is the message.” The second post, focuses on a...

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EDUsummIT 2015 (International Summit on ICT in Education) is a global knowledge building community of researchers, educational practitioners, and policy makers committed to supporting the effective integration of research and practice in the field of ICT in...

Of ballots and names…

Jon Krosnick, a professor at Stanford, argues that Hillary Clinton's surprise victory in the New Hampshire primary (contrary to what was being predicted in the pre-election surveys) could be simply due to the design of the ballot! Here is is the key quote: Our...

Technology, Design & OofSI at E-Learn 2018

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Most of the work that we do at the Office of Scholarship and Innovation at the Teachers College is practical and pragmatic—working with school districts through our community design model, reimagining what university technology labs can be, supporting faculty in their...

Mishra & Hershey, 2004

A few years ago I was invited to be a part of a symposium on etiquette and the design of interactive media (organized by the Association for the Advancement of Artificial Intelligence). I hosted all the papers and presentations from the symposium (links to which I...

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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