Kolam Pattern Generator

A comprehensive mathematical Kolam pattern generator implementing multiple algorithms based on research papers and traditional mathematical foundations.

Project Structure

kolam/
├── backend/                 # Flask API backend
│   ├── app.py              # Main application
│   ├── requirements.txt    # Python dependencies
│   └── README.md          # Backend documentation
├── test-frontend/          # Temporary test frontend (delete after testing)
│   ├── index.html         # Test HTML interface
│   └── README.md          # Frontend test documentation
├── run_backend.bat        # Windows batch file to start backend
└── README.md              # This file

Mathematical Foundation

The Kolam generator implements multiple algorithms based on research papers:

• Algorithm 1: Hridaya Kolam (Chakraborty & Manna, 2025)
• Algorithm 2: Pulli Kolam (Traditional dot-grid patterns)
• Algorithm 3: Rangoli Kolam (Artistic flowing patterns)
• Algorithm 4: Muggulu Kolam (Telugu geometric designs)
• Algorithm 5: Alpana Kolam (Bengali floral motifs)
• Algorithm 6: Kolam Classification (KolamNetV2 inspired)

Core Parameters

• m: Number of dots per arm
• n: Number of arms
• Constraint: gcd(m,n) = 1 (parameters must be coprime)
• Type: Kolam style selection (hridaya, pulli, rangoli, muggulu, alpana)

🔢 Algorithm Details

Algorithm 1: Hridaya Kolam Generation

Source: Chakraborty & Manna (2025) - Algorithm 1

Mathematical Foundation:

• Input: m (number of radial dots), n (number of arms) where gcd(m,n) = 1
• Output: Set of polar coordinates (r, θ) for closed Kolam pattern

Algorithm Steps:

1. Initialize angle step: Δθ = 2π/n
2. Generate sequence S:

   for k = 0 to m-1:
       if k == 0:
           a_k = m
       else:
           a_k = (k × n) mod m
       Append a_k to S
   

3. Form extended sequence S': Repeat S exactly n times
4. Generate coordinates:

   for i = 0 to length(S')-1:
       θ_i = (i mod n) × Δθ
       r_i = S'[i]
       Append point (r_i, θ_i) to C
   

5. Close the loop: Append initial point C[0] at the end

Algorithm 2: Pulli Kolam Generation

Source: Traditional dot-grid patterns

Characteristics: Simple geometric connections, grid-based, linear connections

Algorithm:

1. Generate dot positions: Create radial dot grid
2. Connect consecutive dots: Linear connections within each arm
3. Connect arms: Circular connections between outer dots

Algorithm 3: Rangoli Kolam Generation

Source: Artistic flowing patterns

Characteristics: Flower-like artistic connections, flowing curves, organic shapes

Algorithm:

1. Generate dot positions: Create radial dot grid
2. Create center connections: Connect center dots in flower pattern
3. Add outer ring: Connect consecutive dots in each arm

Algorithm 4: Muggulu Kolam Generation

Source: Telugu geometric patterns

Characteristics: Intricate geometric designs, diamond/square patterns, symmetric connections

Algorithm:

1. Generate dot positions: Create radial dot grid
2. Create geometric patterns: Connect opposite arms in pairs
3. Form diamond shapes: Connect dots in symmetric patterns

Algorithm 5: Alpana Kolam Generation

Source: Bengali floral motifs

Characteristics: Floral, organic patterns, petal-like connections, radial symmetry

Algorithm:

1. Generate dot positions: Create radial dot grid
2. Create petal connections: Connect center to outer dots
3. Form circular pattern: Connect outer dots in circular fashion

Algorithm 6: Kolam Classification (KolamNetV2 Inspired)

Source: Sasithradevi et al. (2024) - KolamNetV2

Classification Rules:

def classify_kolam(m, n):
    if m <= 3:
        return 'pulli', 0.85
    elif m <= 6:
        return 'hridaya', 0.90
    elif m <= 8:
        return 'rangoli', 0.80
    else:
        return 'muggulu', 0.75

Example Patterns

Based on the research papers, here are some valid pattern combinations:

• m=4, n=5: Simple 4-dot pattern (Pulli style)
• m=5, n=8: Classic Hridaya Kolam (Heart-shaped)
• m=6, n=7: 6-dot pattern (Rangoli style)
• m=8, n=9: 8-dot pattern (Muggulu style)
• m=10, n=7: Complex 10-dot pattern (Alpana style)
• m=12, n=5: 12-dot pattern with 5 arms

Key Features

• Multiple Kolam Types: 5 different traditional styles
• Research-Based Algorithms: Based on academic papers
• Pattern Classification: KolamNetV2 inspired classification
• Modular Arithmetic: Algorithm 1 implementation
• Parameter Validation: Coprime constraint checking
• Multiple Connection Styles: Curves, lines
• RESTful API Design: Clean, documented endpoints
• Interactive Test Frontend: Real-time pattern generation
• Mathematical Foundation: Traditional and modern approaches

Mathematical Properties

Coprime Constraint

• Requirement: gcd(m, n) = 1
• Purpose: Ensures proper sequence generation and pattern closure
• Validation: math.gcd(m, n) == 1

Sequence Properties

• Generator Sequence S: Length = m
• Extended Sequence S': Length = m × n
• Pattern Closure: S'[0] = S'[m×n] (circular)

Geometric Properties

• Radial Symmetry: n-fold rotational symmetry
• Scale Invariance: Patterns scale with radius parameter
• Connectivity: Each pattern forms closed loops

Algorithm Selection Guide

Kolam Type	Best For	Characteristics	Complexity
Hridaya	Traditional patterns	Complex curves, mathematical precision	High
Pulli	Simple designs	Grid-based, linear connections	Low
Rangoli	Artistic patterns	Flowing curves, organic shapes	Medium
Muggulu	Geometric designs	Symmetric patterns, angular lines	Medium
Alpana	Floral motifs	Petal-like, radial connections	Medium

Research References

1. **Chakraborty, S. K., & Manna, A. (2025)**. Extending Hridaya Kolam to Even-Ordered Dot Patterns and Their Applications. arXiv preprint arXiv:2507.02874.

2. **Sasithradevi, A., Sabarinathan, S. Shoba, et al. (2024)**. KolamNetV2: efficient attention-based deep learning network for tamil heritage art-kolam classification. Heritage Science, 12, 60.

3. **ResearchGate Publication**. Generation of Kolam-Designs Based on Contextual Array P Systems.