Fun with Functions!

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

1. The butterfly

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

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

This is plotted by the polar equation:

The next 3 were all created by my students.

3.  Chaotic spiral (by Laura Y9)

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

4.  The flower (by Felix Y9)

Some nice rotational symmetries on this one.  Plotted by:

5. The heart (by Tiffany Y9)

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

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