1. Calculating Fractal Dimension from Vector Images Kelly Ran

2. What Is A Fractal?

3. Fractal Dimension Lines: D=1 Squares: D=2 Fractals: Non-integer D Calculated using multiple methods Box-counting dimension

4. Fractal Dimension Applications Texture classification Protein molecule analysis Plant growth analysis Model: plants, particle motion

5. Vector Graphics Raster graphics: pixel-by-pixel Research applications calculate D from raster graphics Vector graphics: Objects like paths and shapes Scalable Vector Graphics (SVG) based on XML Paths

6. SVG Example rect01 - rectangle with sharp corners <rect x="1" y="1" width="1198" height="398" fill="none" stroke="blue" stroke- width="2"/>

7. Goals Is it possible to calculate fractal dimension from vector images? Goals: Calculate D from SVG images Show calculations on a display screen Compare raster v. vector Time? Accuracy?

8. Procedures Create SVG files Inskcape Software Sierpinski Triangle, 3 iterations Sierpinski Triangle, 6 iterations

9. Procedures Processing language Import SVG Array of objects D calculation: size N of grid, number s of grids Hash table: N is key, s is value

15. Testing Line, square Fractals with known fractal dimensions

16. To Be Done Improve upon program Gather more data Implement raster method Linear regression function: linear algebra least squares method