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Introduction

An **L-system**, or Lindenmayer system, is a Turing-complete form of computaion, based in the parallel rewriting of symbols, usually provided and managed as strings. The name comes after Aristid Lindenmayer, a biologist who created it in order to simulate the growth of plants.

An L-system consists of:

:   * An alphabet of symbols
    * An initial string, known as the *axiom*
    * A set of rewriting rules, in he form A → B, where A is a single symbol and B is a string. The B string can contain zero, one or multiple symbols, including A.

Computation

At start, the *current* string is the axiom.

On each step of computation, every symbol Aₙ in the current string, having a rewriting rule Aₙ → Bₙ, is replaced by Bₙ. if the string Bₙ of the rule Aₙ → Bₙ contains the symbol Aₙ, the rule is not applied recursively. This is why this form of computation is called "parallel". Once the rewriting of symbols have been performed, the string was converted to another string, usually longer.

After a defined number of steps, the string is the result of the computation.

Example (rabbit population)

Alphabet: { `I`, `M` } for immature and mature rabbit. Only a mature rabbit can procreate a bunny

Rules:

:   * `I` → `M` (An immature rabbit will be a mature one in the next step)
    * `M` → `MI` (A mature rabbit will procreate a bunny in the next step)

Axiom: `I` (Let us start with a immature rabbit)

Computation (5 steps):

| Step | String | Notes |
| --- | --- | --- |
| 0 | `I` | the axiom |
| 1 | `M` |  |
| 2 | `MI` |  |
| 3 | `MIM` |  |
| 4 | `MIMMI` |  |
| 5 | `MIMMIMIM` | the result |

As you can see, the number of rabbits (the string length) in each step corresponds to the Fibonacci numbers.

Interpretation

It is common to make a further use of the resulting string. For example, symbols can represents musical notes, graphic operations, etc. In this sense, the string is like a program, and each symbol is a instruction of that program.

When using graphic operations, sometimes specific symbols represent turtle graphics operations such as moving forward, moving forward and drawing, turning a certain angle, etc. Other symbols could represent push/pop operations in a stack data structure, in order to save the position/angle of the pen, to be retieved later.

Task

Create a function, method, procedure, class, script, etc. (the solution) to compute the steps of a given L-system, and then, to perform the interpretation of the resulting string.

The inputs of the solution must be:

:   * The axiom
    * The rewritig rules, in a data structure natural to your language, it could be, for example, an array of pairs of strings (S, R) where S is the symbol and R is the :rewriting of the symbol
    * The number of steps to perform
    * The set of operations associated to each symbol of the resulting string, in a natural structure of your language, it could be, for example, an array of pairs (S, O) where S is a symbol and O is a structure that denotes delayed functionallity, such as anonymous functions, callbacks, pointers to functions, names of functions that can be invoked at run time with EVAL, lambda expressions, etc. (list is not exhaustive)

It is highly recommended for the solution to be absracted enought to let the inputs to be given separated from the solution, this is, the solution should be coded as its final place is inside a library which is invoked with specific values or parameters. It is not required for the solution to contain the necessary code be an actual library, it is enough that the code of the solution is separarted from the code of the invocation.

**Accesing environment objects**. When interpretation produces graphical output, it is common to have objects that operations should access, such as graphic handlers, a stack, etc. A solution is to define the operations requestng such objects as parameters. Another (maybe better) option is to use closures.

If there already exists a library, package, etc. for your language to perform execution of L-systems, indicate the name of the library, how to get it, if it is open source, and examples of how to use it (see below).

Test cases

Provide one or more test cases of L-systems executed and interpreted by your solution.

References

:   * Wikipedia: L-system
assistant
L-system functionality as a Role that may be mixed in to a scalar.

```
# L-system functionality 
role Lindenmayer {
    has %.rules;
    method succ {
        self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules)
    }
}

# Testing
my $rabbits = 'I' but Lindenmayer({I => 'M', M => 'MI'});

.say for $rabbits++ xx 6;

```

Output:

```
I
M
MI
MIM
MIMMI
MIMMIMIM
```

Also see:  
Dragon\_curve#Raku  
Hilbert\_curve#Raku  
Koch\_curve#Raku  
Peano\_curve#Raku  
Penrose\_tiling#Raku  
Sierpinski\_curve#Raku  
Sierpinski\_arrowhead\_curve#Raku  
Sierpinski\_square\_curve#Raku  
among others...