Calculating Fractal Dimension from Vector Images

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Calculating Fractal Dimension from Vector Images
Kelly Ran
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What Is A Fractal?
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Fractal Dimension

• Lines D1
• Squares D2
• Fractals Non-integer D
• Calculated using multiple methods
• Box-counting dimension

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Fractal Dimension Applications

• Texture classification
• Protein molecule analysis
• Plant growth analysis
• Model plants, particle motion

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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

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SVG

• lt?xml version"1.0" standalone"no"?gt
• ltdescgtExample rect01 - rectangle with sharp
  cornerslt/descgt
• ltrect x"1" y"1" width"1198" height"398"
• fill"none" stroke"blue"
  stroke-width"2"/gt
• lt/svggt

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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?

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Procedures

• Create SVG files
• Inskcape Software

Sierpinski Triangle, 3 iterations
Sierpinski Triangle, 6 iterations
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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

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Testing

• Line, square
• Fractals with known fractal dimensions

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To Be Done

• Improve upon program
• Gather more data
• Implement raster method
• Linear regression function linear algebra least
  squares method