LSystemExamples is a package that exports 12 examples of Lindenmayer Systems that are ready for use with the LSystemPlot and Iterate commands.

The 12 exported Lindenmayer Systems:

$\mathrm{SierpinskiTriangle}$

$\mathrm{Tree}$

$\mathrm{KochCurve}$

$\mathrm{FractalPlant}$

$\mathrm{DragonCurve}$

$\mathrm{GosperCurve}$

$\mathrm{Box}$

$\mathrm{Seaweed}$

$\mathrm{Crystal}$

$\mathrm{Rings}$

$\mathrm{Carpet}$

$\mathrm{PenroseTiling}$

Each example is itself a module with four exports:

$\mathrm{IterationRules}$, $\mathrm{InitialState}$, $\mathrm{PlottingConstants}$, and $\mathrm{InitialAngle}$

$\mathrm{IterationRules}$ defines the rules of the LSystem Iteration process.

$\mathrm{InitialState}$ defines the Initial String of the LSystem.

$\mathrm{PlottingConstants}$ defines the plotting procedures that each character represents.

$\mathrm{InitialAngle}$ defines the initial plotting angle of the LSystem.

These exports can be given to LSystemPlot, and Iterate directly as input (for the respective parameters).

LSystemExamples also exports three functions:

$\mathrm{PlotExample}$, $\mathrm{ViewStateAsString}$, $\mathrm{ViewRulesAsStrings}$.

$\mathrm{PlotExample}$ accepts an exported LSystem example and an optional positive integer (the default value is 1) to specify how many times the iteration rule will be applied to the initial state. $\mathrm{PlotExample}$ returns a plot of the LSystem.

$\mathrm{ViewStateAsString}$ accepts an LSystem state and prints the string representing the state.

$\mathrm{ViewRulesAsStrings}$ accepts a table of LSystem rules and prints the rules as a list(string=string).

$\mathrm{with}\left(\mathrm{Fractals}:-\mathrm{LSystem}\right)\:$

$\mathrm{with}\left(\mathrm{LSystemExamples}\right)\:$

$\mathrm{LSKoch}≔\mathrm{KochCurve}$

$\mathrm{LSKoch}≔\mathrm{KochCurve}$

$\mathrm{ViewStateAsString}\left(\mathrm{LSKoch}:-\mathrm{InitialState}\right)$

$''F''$

$\mathrm{ViewRulesAsStrings}\left(\mathrm{LSKoch}:-\mathrm{IterationRules}\right)$

$\left[''F''=''F+F-F-F+F''\right]$

$\mathrm{PlotExample}\left(\mathrm{LSKoch}\right)$

$\mathrm{PlotExample}\left(\mathrm{LSKoch}\,6\right)$

$\mathrm{LSGosperCurve}≔\mathrm{GosperCurve}$

$\mathrm{LSGosperCurve}≔\mathrm{GosperCurve}$

$\mathrm{ViewStateAsString}\left(\mathrm{LSGosperCurve}:-\mathrm{InitialState}\right)$

$''X''$

$\mathrm{ViewRulesAsStrings}\left(\mathrm{LSGosperCurve}:-\mathrm{IterationRules}\right)$

$\left[''Y''=''+X-YY--Y-X++X+Y''\,''X''=''X-Y--Y+X++XX+Y-''\right]$

$\mathrm{PlotExample}\left(\mathrm{LSGosperCurve}\right)$

$\mathrm{PlotExample}\left(\mathrm{LSGosperCurve}\,5\right)$

The Fractals:-LSystem:-LSystemExamples package was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.