# MathLapse- L- System for Single Knot Kolam Pattern Generation

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## Licence

## Credits

- Design and Development

In the art form of SUZHI KOLAM/ KAMBI KOLAM, dots called pulli are arranged in rhombic, square, triangular, or free shapes, and a single, uninterrupted linear or curvilinear line, called the kambi, intertwines the dots.

L-System

Lindermayer system is a parallel rewriting system and a type of formal grammar. It consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols.

The recursive nature of L system rules leads to self similarity and thereby fractal like forms are easy to describe with an L system. This nature is applied in generating kolam pattern. Kolam pattern becomes more complex by increasing the iteration level.

Software: Python Turtle Graphics

*SUZHI / KAMBI / SIKKU Kolam*

In the art form of SUZHI KOLAM/ KAMBI KOLAM, dots called pulli are arranged in

rhombic, square, triangular, or free shapes, and a single, uninterrupted linear or curvilinear line,

called the kambi, intertwines the dots. While there are no written or verbally stated rules. Listed

some rules of pulli(dots) and kambi/Suzhi kolam from examining the designs (Yanagisawa,

Nagata, Robinson Thamburaj). Rules can be added / removed.

Rule 1: Uniformly spacing of dots

Rule 2: Smooth drawing line around the dots

Rule 3: Symmetry in drawings

Rule 4: Straight lines are drawn inclined at an angle of 45 degrees

Rule 5: Drawing lines never trace back

Rule 6: Arcs adjoining the dots

Rule 7 : Kolam is completed when all points are enclosed by the drawing line

Kolam drawing can be treated as a special kind of a graph with the crossings considered

as vertices and the parts of the kambi between vertices treated as edges. The only restriction is

that unlike in a graph, these edges cannot be freely drawn as there is a specific way of drawing

the kolam. The single kambi kolam will then be an Eulerian graph with the drawing starting and

ending in the same vertex and passing through every edge of the graph only once. Single knot

kolam also called as “ANTHATHI Kolam” in Tamil Nadu. The Smooth line starts at a point and

end in the same point. Single knot kolam can be drawn for any type of dot structure (rhombic,

square, triangular, or free shapes).

L-System

Lindermayer system is a parallel rewriting system and a type of formal grammar. It consists of

an alphabet of symbols that can be used to make strings, a collection of production rules that

expand each symbol into some larger string of symbols.

The recursive nature of L system rules leads to self similarity and thereby fractal like forms are

easy to describe with an L system. This nature is applied in generating kolam pattern. Kolam

pattern becomes more complex by increasing the iteration level.

Software: Python Turtle Graphics**Applying L-System for Kolam pattern Generation:**

Procedure:

Axiom or Initiator: FBFBFBFB

Rules: A AFBFA

B AFBFBFBFA

Angle: 45^{o}

From current cursor position ,

F Forward 10 units (draw a line 10 units length)

A Draw an arc (circle (10, 90))

B Calculate forward units I = 5/sqrt (2)

Forward I Units

Draw an arc (circle (I, 270))

Forward I Units