Let's start with the basics, if we take a definition from the well-known and beloved Wikipedia, then the L-system (or Lindenmayer's system ) is a parallel rewriting system and a form of formal grammar.
In simple terms, the L-system consists of an alphabet of characters that can be used to create strings, a set of generative rules that specify substitution rules for each character, an initial string ( "axiom" ), with which the construction begins, and a translation mechanism formed by lines in geometric structures. The simplest example of an L-system is the tree construction problem.
Input data:
String ( hereinafter Axiom ): AB
Variables ( which we can use in building the tree ): ABC
Rule (the rule by which each variable on the next line changes ):
A -> AB
B -> AC
C -> A
The following transformations are obtained:
Generation |
condition |
|---|---|
one |
AB |
2 |
AB AC |
3 |
AB AC AB A |
4 |
AB AC AB A AB AC AB |
five |
AB AC AB A AB AC AB AB AC AB A AB AC |
6 |
etc… |
The main direction in which L-systems are used is modeling the growth processes of both living organisms and inanimate objects (crystals, mollusk shells or honeycombs) .
Example:
To simulate such processes, we will use a programming language such as Python, which has a built-in "turtle" library .
So let's get started:
Here we are importing the Turtle library into our project:
import turtle
Next, we include all the necessary configurations for our turtle :
turtle.hideturtle()
turtle.tracer(1)
turtle.penup()
turtle.setposition(-300,340)
turtle.pendown()
turtle.pensize(1)
, :
axiom = "F+F+F+F"
tempAx = ""
itr = 3
(itr- , )
, itr-, "" /:
for k in range(itr):
for ch in axiom:
if ch == "+":
tempAx = tempAx + "+"
elif ch == "-":
tempAx = tempAx + "-"
elif ch == "F": #F
tempAx = tempAx + "F+F-f-F+F"
else:
tempAx = tempAx + "f"
axiom = tempAx
tempAx = " "
print(axiom)
, "+":
if ch == "+":
tempAx = tempAx + "+"
( ) “+” “+” . “-” “f”, “-” “f” . “F”, “F + F – f – F + F”, . , “”, . :
axiom = tempAx
tempAx = " "
( ):
, , . , :
for ch in axiom:
if ch == "+":
turtle.right(45)
turtle.forward(10)
turtle.right(45)
elif ch == "-":
turtle.left(45)
turtle.forward(10)
turtle.left(45)
else:
turtle.forward(20)
, , "+", "-", "F" "f". , "+":
if ch == "+":
turtle.right(45)
turtle.forward(10)
turtle.right(45)
, 45 , , 10, , 45 . "-":
elif ch == "-":
turtle.left(45)
turtle.forward(10)
turtle.left(45)
, "+", , . "F" "f", 20 :
else:
turtle.forward(20)
-:
-, :
turtle.fillcolor("#99BBFF")
turtle.begin_fill()
#99BBFF - (RGB: 153, 187, 255), begin_fill() . , , :
turtle.end_fill()
turtle.update()
turtle.done()
end_fill() . "". -:
, "" , .
In the end, I also want to add that I really enjoyed working and writing on this topic, perhaps in the future, I will write a number of articles on the topic of "L-systems", but in the meantime, I want to present you the results of my poking creativity: