The Beautiful Walk of the Penguin

Journal entry for 14 Jun 2010 | Link

In Pynguin, a Python implementation of turtle graphics, one can write a function that takes an angle and a length, points the penguin at the given angle, and draws a line of the stated length.

Easy enough.

vector(120,100)

Using vector(), one can write a function that takes an an angle and a length, draws a line at that angle times 0, then a line at that angle times 1, then 2, and keeps going indefinitely. ("turn += 1" is the same as "turn = turn + 1".)

This will result in polygons of various kinds depending on what angle you feed into the function. (After a while the penguin starts drawing over old lines.) If the angle is 90° you get a square.

poly(90,100)

At 120° you get a triangle.

poly(120,100)

60° is a hexagon.

poly(60,100)

144° is a five-pointed star.

poly(144,100)

80° is a nine-pointed star. (80 * 9 = 144 * 5 = 720, which tells you something about stars.)

poly(80,100)

A turn of one and a length of one plugged into this function results in a circle. (Really, a 360-sided polygon, but close enough for a penguin.)

poly(1,1)

We can alter poly() to take two different vectors, draw the first, draw the second, and then increment the multiplier on the angle as before.

This allows us to ask a question: what do you get when you cross a triangle with a square? (Which I guess we could ask anyway, but this allows us to ask with a reasonable expectation of an answer.)