Turtle graphics

Turtle graphics is a term in computer graphics for a method of programming vector graphics using a relative cursor (the "turtle") upon a Cartesian plane. Turtle graphics is a key feature of the Logo programming language.

Overview

A spiral drawn with an iterative turtle-graphics algorithm

The turtle has three attributes:

1. a position
2. an orientation
3. a pen, itself having attributes such as color, width, and up versus down.

The turtle moves with commands that are relative to its own position, such as "move forward 10 spaces" and "turn left 90 degrees". The pen carried by the turtle can also be controlled, by enabling it, setting its color, or setting its width. A student could understand (and predict and reason about) the turtle's motion by imagining what they would do if they were the turtle. Seymour Papert called this "body syntonic" reasoning.

From these building blocks one can build more complex shapes like squares, triangles, circles and other composite figures. Combined with control flow, procedures, and recursion, the idea of turtle graphics is also useful in a Lindenmayer system for generating fractals.

Turtle geometry is also sometimes used in graphics environments as an alternative to a strictly coordinate-addressed graphics system.

History

Turtle graphics were added to the Logo programming language by Seymour Papert in the late 60s to support Papert's version of the turtle robot, a simple robot controlled from the user's workstation that is designed to carry out the drawing functions assigned to it using a small retractable pen set into or attached to the robot's body. Turtle geometry works somewhat differently from (x,y) addressed Cartesian geometry, being primarily vector-based (i.e. relative direction and distance from a starting point) in comparison to coordinate-addressed systems such as PostScript. As a practical matter, the use of turtle geometry instead of a more traditional model mimics the actual movement logic of the turtle robot. The turtle is traditionally and most often represented pictorially either as a triangle or a turtle icon (though it can be represented by any icon).

Papert's daughter, Artemis, has been using turtle graphics to explore the relationship between art and algorithm.

Example

The following actions generate the figure to the right, assuming a turtle initially in the center, pointed towards the top of the page and the pen is down.

• repeat four times:
  • turn right 90 degrees
  • move forward 100 steps
• then move forward 100 steps again

Extension to Three Dimensions

The ideas behind turtle graphics can be extended to include three-dimensional space. This is achieved by using one of several different coordinate models. If the turtle operates in cylindrical coordinates, then it has a location and a heading within its plane, and its plane may be rotated around the vertical axis. This often manifests itself as the turtle having two different heading angles, one within the plane and the other determining the plane's angle. Usually changing the plane's angle does not move the turtle.

Other coordinate models may also be used. For a more complete discussion of three-dimensional turtle coordinate systems and some examples of each, see Cheloniidae Turtle Graphics.

See also

• Turtle (robot)
• Logo (programming language)
• Python turtle module
• PythonTurtle - Standalone application
• KTurtle
• Cheloniidae Turtle Graphics
• Starlogo
• One Laptop per Child's XO-1 contains a Turtle Art activity for playing with turtle graphics
• L-system

Further reading

• Abelson and diSessa. Turtle geometry: the computer as a medium for exploring mathematics. Cambridge, MA: MIT Press, 1981.

External links

• "Web Turtle", turtle graphics in a web page, by Bill Kendrick, author of Tux Paint
• Art created with turtle graphics by Artemis Papert
• A turtle graphics language and pattern gallery
• "3D Flying Pipe-laying Turtle" by Tom Verhoeff from The Wolfram Demonstrations Project (retrieved on 2009-01-31)
• "Turtle Graphics", Turtle Graphics written in MGrammar, by Jason Hogg
• Turtle Art website maintained by Brian Silverman and Artemis Papert
• Turtle Art activity included in the Sugar learning platform