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CSE 423 Computer Graphics | MUSHFIQUR ROUF CSE423:

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Presentation on theme: "CSE 423 Computer Graphics | MUSHFIQUR ROUF CSE423:"— Presentation transcript:

1 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 CSE423: Computer Graphics Fractals Mushfiqur Rouf nasarouf@gmail.com

2 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Fractal Arbitrarily fine structure Irregularity Self-similarity Fractional dimension Recursive Definition

3 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Dimension Number of independent parameters needed to describe a point

4 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Fractional Dimension how completely a fractal appears to fill space

5 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Self Similarity

6 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Examples

7 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Koch Snowflake

8 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Koch Snowflake: Construction

9 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Von Koch Curve Generic Koch Specify an angle, not just 45º Dimension = An Example, for 85º  How would a 90º curve look like?

10 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Quadratic Koch

11 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Quadratic Koch

12 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Gosper Curve

13 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://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)

14 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Hilbert Curve Dimension = 2

15 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Hilbert Curve 3D

16 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Peano Curve

17 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Dragon Curve

18 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Dragon Curve

19 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Dragon Curve

20 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Dragon Curve: Self Similarity

21 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Dragon Curve: Construction

22 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Sierpinski Triangle

23 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Sierpinski Triangle: Construction or Destruction

24 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Sierpinski Triangle: Self-Similarity

25 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Sierpinski Tetrahedron: 3D Extension to Sierpinski Triangle

26 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Sierpinski Carpet

27 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Menger Sponge

28 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Menger Sponge: Construction

29 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 T-Box Curve

30 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 T-Box Curve

31 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Hexaflake

32 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Apllonian Gasket

33 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Random Fractal: Brownian Tree

34 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Random Fractal: Brownian Tree

35 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Random Fractal: Mountain

36 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Mandelbrot Set

37 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423 Mandelbrot Set: Self Similarity

38 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

39 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

40 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

41 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

42 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

43 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

44 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

45 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

46 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

47 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

48 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

49 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

50 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

51 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

52 CSE 423 Computer Graphics | MUSHFIQUR ROUF nasarouf@gmail.com http://groups.google.com/group/cse423spring07/ http://faculty.bu.ac.bd/~rouf/cse423

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