My most recent mathart animation was the latest in a series looking at the regions formed by rotating overlapping shapes:

Mary Gentry contacted me to ask for some insight into how it was created:

This particular graph involved quite a few different techniques which I had used in previous work. These are all strategies that I have developed through many hours of play and experimentation with Desmos, as well as by collaborating with and being inspired by other Twitter Desmos artists, such as Dan Anderson, Suzanne von Oy and Luke Walsh.

Follow the links below for details of some of the steps in the process:

## Creating an array

## Rotating a graph about a point

## Shading regions defined by multiple inequalities

## Expressing polar graphs in Cartesian form

## The final graph

The animation that I posted was then made by adding frames individually on Gifsmos.

Finally, my number one tip for creating art in Desmos is to set yourself challenges and start playing!

This is an amazing resource. Thanks for taking the time to put it together. I may be back with questions! I’m wondering if we can turn it into a Desmos activity.

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A Desmos activity is probably what it should’ve been – in my mind before I wrote it I envisaged more text in the body of the blog and a couple of little Desmos explainers, but in the end it was easier to just write most of it within Desmos graphs, so a full-on Desmos activity would’ve worked better.

Perhaps I’ll do an activity with an assortment of little tips like this at some point, since there seem to be many more people interested in it than I imagined there would be!

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And thank you for your kind words!

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