This post is inspired by the Quora thread on interesting functions to plot.

  1. The butterfly

Screen Shot 2017-11-16 at 8.28.17 PM

This is a slightly simpler version of the butterfly curve which is plotted using polar coordinates on Desmos as:

Screen Shot 2017-11-16 at 8.32.57 PM

Polar coordinates are an alternative way of plotting functions – and are explored a little in HL Maths when looking at complex numbers. The theta value specifies an angle of rotation measured anti-clockwise from the x axis, and the r value specifies the distance from the origin. So for example the polar coordinates (90 degrees, 1) would specify a point 90 degrees ant clockwise from the x axis and a distance 1 from the origin (i.e the point (0,1) in our usual Cartesian plane).

2. Fermat’s Spiral

Screen Shot 2017-11-16 at 8.28.26 PM

This is plotted by the polar equation:

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The next 3 were all created by my students.

3.  Chaotic spiral (by Laura Y9)

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I like how this graph grows ever more tangled as it coils in on itself.  This was created by the polar equation:

Screen Shot 2017-11-16 at 8.44.56 PM

4.  The flower (by Felix Y9)

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Some nice rotational symmetries on this one.  Plotted by:

Screen Shot 2017-11-16 at 8.45.03 PM

5. The heart (by Tiffany Y9)

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Simple but effective!  This was plotted using the usual x,y coordinates:

Screen Shot 2017-11-16 at 8.45.09 PM

You can also explore how to draw the Superman and Batman logos using Wolfram Alpha here.