# Python Challenge 1 - concertina

### Hints for Python Challenge 1

• If you are having diﬃculties plotting a circle, try plotting a simple function ﬁrst and build up to more complex functions. For example, maybe try plotting the straight line y = 2x + 1 ﬁrst, or the quadratic y = x2 − 1.

• When you are plotting the circle, the parameter t needs to be chosen. Usually this is chosen as an array. Such a array can be set up using the numpy.linspace command.

• The equation describing Fermat’s Spiral is given by

y = ±t1/2 sin(t)
x = ±t1/2 cos(t)

(where ± means that one part of the spiral uses + and one uses −). Can you work out how to plot the curve using just one plot command?

• The equation describing the Butterﬂy Curve includes the exponential function. This function is coded within numpy as numpy.exp. Also, the number π can be obtained using numpy.pi.

#### Notes

In the figures plotted above, a number of Colormaps have been used to vary the colour of the line segments as a function of position. Different maps have different purposes - some are smoothly graded from light to dark, while others only appear as discrete colours.