L-System Viewer

A viewer for Lindenmayer Systems written in Python / Pygame.

Lots of inspiration is taken from Fractint's L-System implementation.

L-System

An L-System is defined by three properties:

• An axiom, eg A
• A set of replacement rules, eg (A -> AB), (B -> A)
• An angle, eg 4

The angle is defined by an integer number of turns that make up 360 degrees, for example:

• 3 is equivalent to 120 degrees per turn
• 4 is equivalent to 90 degrees per turn
• 36 is equivalent to 10 degrees per turn

Equivalently, the angle in degrees per turn is 360 / angle

Graphics State

The graphics state at any point during the drawing process is defined as follows:

• x, the x position of the turtle
• y, the y position of the turtle
• theta, an angle in degrees
• phi, an angle in degrees
• length, the drawing length, in arbitrary units
• reverse, true if an odd number of ! command have been encountered
• colour, an index into a colour palette

Drawing Commands

• F: Draw forward using angle theta
• G: Move forward using angle theta
• D: Draw forward using angle phi
• M: Move forward using angle phi
• -: Turn left by 360/angle (subtract 360/angle from theta)
• +: Turn right by 360/angle (add 360/angle to theta)
• [: Save the current graphics state to the graphics stack
• ]: Restore the topmost graphics state from the graphics stack
• !: Reverse the meaning of + and -, and \ and /
• |: Turn 180 degrees (or as close as possible if angle is odd)
• \{NUM}: Turn left {NUM} degrees relative to phi
• /{NUM}: Turn right {NUM} degrees relative to phi
• <{NUM}: Decrement the current colour index by {NUM}
• >{NUM}: Increment the current colour index by {NUM}
• C{NUM}: Set the current colour index to {NUM}
• @{NUM}: Scale length by a factor of {NUM}

Where {NUM} is a positive number in decimal, optionally preceded by q and/or i, which represent the square root and inverse (respectively) of the decimal number.

The decimal place may be omitted in the case of integers. In the case where the decimal place is included, leading or trailing digits may be omitted if they are zero, ie .5 and 0.5 are equivalent, and 5.0, 5. and 5 are all equivalent.

• q2 evaluates to approx 1.414, ie sqrt(2)
• i2 evaluates to 0.5, ie 1/2
• iq2 evaluates to approx 0.707, ie 1/sqrt(2)
  • This is equivalent to qi2, since 1/sqrt(n) === sqrt(1/n)