roguh / hturtle

Hyperbolic Turtle Graphics is a python tool to explore hyperbolic geometry in the Poincaré disk model. It is based on the turtle standard library module. Basically one interacts with a "turtle" as in the Logo programming language but the instructions of moving forward or turning are carried out with respect to the Poincaré metric.

Hyperbolic Turtle Graphics

Hyperbolic Turtle Graphics is a LOGO type program where the turtle moves in the Poincaré disk model of the hyperbolic plane.

Right now the code is terrible, including use of a global variable named i (which will conflict with typical variables used in for loops).

However, it works and can be used to produce some nice pictures and learn some geometry.

Example usage

Example usage:

From IDLE

    >>> import os
    >>> os.chdir('the directory containing hturtle.py')
    >>> import hturtle
    >>> hturtle.forward(1)
    >>> hturtle.right(90)
    >>> hturtle.forward(1)
    >>> hturtle.right(90)
    >>> hturtle.forward(1)
    >>> hturtle.right(90)
    >>> hturtle.forward(1)
    >>> hturtle.right(90)
    >>> hturtle.right(90)
    >>> hturtle.screenshot('screenshot1')

This generates the file 'screenshot1.eps' containing the following image:

Relationship to the turtle standard library

This program is built on the turtle library which is imported as turtle. For example:

    >>> hturtle.reset()
    >>> hturtle.turtle.pencolor('brown')
    >>> hturtle.regularwalk(1,90,20)
    >>> hturtle.screenshot('screenshot2')

Other functions

There are several functions in hturtle.py which are for internal use. The ones meant for interacting with the turtle are: reset, right, randomwalk, regularwalk, screenshot, side, forward, path, and allwalk.

    >>> hturtle.reset()
    >>> for s in range(5,20):
	hturtle.regularwalk(hturtle.side(s),90,s)
    >>> hturtle.screenshot('screenshot3')

    >>> hturtle.reset()
    >>> hturtle.turtle.pencolor('blue')
    >>> hturtle.randomwalk(0.1,[-90,0,90,180],1000)
    >>> hturtle.screenshot('screenshot4')

Have fun!