Auto-Generation System Based on Fractal Geometry for Batik Pattern Design
Abstract
:Featured Application
Abstract
1. Introduction
2. Related Work
2.1. Fractal Geometry
- Self-similarity, which may include precise self-similarity—the same at all scales; quasi-self-similarity—similar patterns on different scales, where small copies of the entire fractal may contain distorted and degenerate forms; statistical self-similarity—random repetition of a pattern so that a number or statistical measurement remains across scales [7]; qualitative self-similarity—such as time series [8]; or multifractal scaling [9,10,11,12]—represented by multiple fractal dimensions or scaling rules.
- Fine or detailed structure on any small scale. The result of this structure is that fractals may have emergent properties [13].
- Local and global irregularities are not easily described in traditional Euclidean geometric languages. For images of fractal patterns, this has been expressed by phrases such as “smoothly stacked surfaces” and “whirlpools on vortices” [14].
- Strange attractors—use iterations of a map or solutions of a system of initial-value differential or difference equations that exhibit chaos.
- Escape-time fractals—use a formula or recurrence relation at each point in a space (such as a complex plane); usually quasi-self-similar; also known as “orbit” fractals.
- Random fractals—use stochastic rules.
2.2. Fractal Pattern Generation
3. Fractal Characteristics of Batik Patterns and Fractal Algorithms
3.1. Fractal Characteristic of Batik Flower Patterns
3.2. Iterated Function System
4. Auto-Generation Algorithm Based on Fractal Geometry
4.1. Generating the Flower-Leaves Pattern
4.2. Generating the Petals Pattern
4.3. Generating the Pistils Pattern
4.4. Generating the Flower-Core Pattern
4.5. Generating the Flower Pattern Layout
5. Experiment and Analysis
5.1. Setting Parameters to Generate Flower Patterns
5.2. Setting Parameters to Generate Layout Patterns of Flowers
6. System Implementation
7. Analysis
8. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Basic Features | Evaluation Parameter |
---|---|
Elements number | 1, 2, 3, multi |
Positional relationship | Rotation, translation |
Symmetry | None, 1/2, 1/3, 1/4, …, rotation |
Petals layers number | Single, double, multi |
Petal shape | Rhombus, curved, wavy |
Petals number/layer | 6, 7, 8, 9, 10, or more |
Pistils number/petal | None, 1, 2, multi |
Flower Pattern | Generation | Original |
---|---|---|
Flower 1 | 2, rotation, 1/8, single, curved, 8, 1 | 2, rotation, 1/8, single, curved, 8, 1 |
Flower 2 | 3, rotation, 1/8, single, wavy, 8, 2 | 3, rotation, 1/8, single, wavy, 8, 2 |
Flower 3 | 2, rotation, 1/8, single, rhombus, 8, 2 | 2, rotation, 1/8, single, rhombus, 8, 2 |
Flower 4 | 2, rotation, 1/6, double, curved, 6, 2, | 2, rotation, 1/6, double, curved, 6 and 12, 4 and 5 |
Flower 5 | 2, rotation, 1/8, single, curved, 8, multi | 2, rotation, 1/8, single, curved, 8, multi |
Flower 6 | 2, rotation, none, multi, curved, 10 or more, none | 2, rotation, 1/3, multi, curved, 10 or more, none |
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Tian, G.; Yuan, Q.; Hu, T.; Shi, Y. Auto-Generation System Based on Fractal Geometry for Batik Pattern Design. Appl. Sci. 2019, 9, 2383. https://doi.org/10.3390/app9112383
Tian G, Yuan Q, Hu T, Shi Y. Auto-Generation System Based on Fractal Geometry for Batik Pattern Design. Applied Sciences. 2019; 9(11):2383. https://doi.org/10.3390/app9112383
Chicago/Turabian StyleTian, Guidong, Qingni Yuan, Tao Hu, and Yi Shi. 2019. "Auto-Generation System Based on Fractal Geometry for Batik Pattern Design" Applied Sciences 9, no. 11: 2383. https://doi.org/10.3390/app9112383