beauty in recursion, fractals gur saran adhar computer science department
TRANSCRIPT
![Page 1: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/1.jpg)
Beauty in Recursion, Fractals
Gur Saran AdharComputer Science Department
![Page 2: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/2.jpg)
A simple example in Recursion‘H-tree’
![Page 3: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/3.jpg)
H-tree level 2
![Page 4: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/4.jpg)
H-tree level 3
![Page 5: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/5.jpg)
Recursion (key idea)
• Letter ‘H’ is an H-tree • An H-tree attached to each end of an H-tree is
also an H-treeDefine an object in terms of copies of itself
![Page 6: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/6.jpg)
Recursion in Mathematics
![Page 7: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/7.jpg)
Iteration vs. Recursion
int Product(int n) //iteration { int i, result =1; for ( i = 1; i <= n; i++) result = result*i; return(result)}
int Product(int n)//recursion
{ if ( n ==1) return (1); else return(n*Product(n-1)); }
![Page 8: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/8.jpg)
Quad Tree Representation of a region
![Page 9: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/9.jpg)
Snowflake (Koch Curve)
![Page 10: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/10.jpg)
Fractal Dimension
D = ln(n)/ ln(1/s)
Higher dimension exhibits more jagged surfacesFor snowflake D = ln(4)/ln(3) = 1.26
![Page 11: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/11.jpg)
Fern
![Page 12: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/12.jpg)
Describing a Branch B A[B]AA(B)
![Page 13: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/13.jpg)
Language of Recursion
• Describing a tree Rules A AA
B A[B]AA(B)
![Page 14: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/14.jpg)
First Tree from grammar
![Page 15: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/15.jpg)
Trees
![Page 16: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/16.jpg)
Mountains
![Page 17: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/17.jpg)
More mountains
![Page 18: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/18.jpg)
Structure of Clouds (NASA)
in marine stratocumuluson on July 7, 1987. First few frames showing the transition from GOES 1 km to Landsat 0.03 km resolution, and then zoom in by 7 successive factors of 2, to see that what's inside a GOES pixel can look rather similar to what's inside the full 500 km gridbox. This so-called "self-similarity" of clouds is characteristic of fractals.
![Page 19: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/19.jpg)
Clouds
![Page 20: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/20.jpg)
lightening
![Page 21: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/21.jpg)
Leaf
![Page 22: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/22.jpg)
Coastline
![Page 23: Beauty in Recursion, Fractals Gur Saran Adhar Computer Science Department](https://reader035.vdocuments.site/reader035/viewer/2022081801/551818e05503469d318b472b/html5/thumbnails/23.jpg)
waterfall