Post on 21-Jan-2016
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE423: Computer Graphics
Fractals
Mushfiqur Roufnasarouf@gmail.com
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Fractal
• Arbitrarily fine structure
• Irregularity
• Self-similarity
• Fractional dimension
• Recursive Definition
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Dimension
• Number of independent parameters needed to describe a point
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Fractional Dimension
• how completely a fractal appears to fill space
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Self Similarity
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Examples
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Koch Snowflake
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Koch Snowflake: Construction
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Von Koch CurveGeneric Koch
• Specify an angle, not just 45º
• Dimension =
• An Example, for 85º • How would a 90º curve
look like?
cos12ln
4ln
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Quadratic Koch
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Quadratic Koch
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Gosper Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Space Filling Curves
• Constructed using line segments only
• But each has dimension = 2
• Contain the entire 2-dimensional unit square – (or the 3-dimensional unit cube, or n-dimensional
hypercube)
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Hilbert CurveDimension = 2
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Hilbert Curve 3D
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Peano Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Dragon Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Dragon Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Dragon Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Dragon Curve: Self Similarity
22ln
2ln
Dimension
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Dragon Curve: Construction
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Sierpinski Triangle
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Sierpinski Triangle: Construction or Destruction
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Sierpinski Triangle: Self-Similarity
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Sierpinski Tetrahedron:3D Extension to Sierpinski
Triangle
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Sierpinski Carpet
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Menger Sponge
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Menger Sponge: Construction
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
T-Box Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
T-Box Curve
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Hexaflake
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Apllonian Gasket
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Random Fractal: Brownian Tree
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Random Fractal: Brownian Tree
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Random Fractal: Mountain
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Mandelbrot Set
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
Mandelbrot Set: Self Similarity
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423
CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.comhttp://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423