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I am building an Android library with different kinds of progress views represented with curves. As you can see it in the gif below, I have used the following curves: Lemniscate of Bernoulli, Lemniscate of Gerono, Epitrochoid, Hypotrochoid, Heart curve and Cannabis curve (not in the gif) :).

Curves

Could you suggest some other curves that could be used in this library? Curve has to be periodic, and to have not that complicated parametric representation (so calculation would be fast).

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    Maybe an astroid ( https://en.wikipedia.org/wiki/Astroid ) ? I guess a circle would be a typical periodic curve, but maybe that's too standard for this app? :) – 2017-01-23
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    Astroid can be done using Hypotrochoid for R = a, r = a/4, d=a. And cycle is too standard. Every progress view is cycle :). – 2017-01-23
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    Very spirograph-like..., but the heart. – 2017-01-23
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    [Lissajous](https://en.wikipedia.org/wiki/Lissajous_curve) curves (and plane projections of their higher-dimensional analogues) are appealing. <> Though this is a nifty library you're building, I think the question is not on-topic ("Opinion-based", or "Not about Mathematics") for Math.SE. Not voting to close, however. – 2017-01-23
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    @VladimirJovanović A plethora of possibilities with polar differential equations / odes.. – 2017-01-23
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    I was not sure, should I ask it on SO or here, but I thought that there is better chance that mathematician will help me. I will try Lissajous curves to see how it looks like. Library is open-source an you can find it [here](https://github.com/vlad1m1r990/Lemniscate). And thanks @AndrewD.Hwang :) – 2017-01-23
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    Don't forget epicycloids and hyperepicycloids – 2017-01-23
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    @DavidQuinn Those are same as Epitrochoid and Hypotrochoid for r=d – 2017-01-23
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    The choice of having a large linewidth somewhat limits the curves you can display. Otherwise, think to the **spirals** (Archimedes' or logarithmic), and the (cousin) important involute of a circle (https://en.wikipedia.org/wiki/Involute). See also the rich (french) site: (http://www.mathcurve.com/courbes2d/developpantedecercle/developpantedecercle.shtml) – 2017-01-23
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    @JeanMarie Everything is changeable. Line length, width, color, every param in every equation. Gif is just example. I will try those curves. Thanks :). – 2017-01-24

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