recapitulation - iit delhi
TRANSCRIPT
![Page 1: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/1.jpg)
Recapitulation
• Exhibit infinite detail • Show self-similarity • Generating approach
recursive procedure deterministic
• Fractal dimension (D) roughness & filling-ness
![Page 2: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/2.jpg)
Recapitulation
![Page 3: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/3.jpg)
Recapitulation
P1 = F(P0) P2 = F(P1)=F(F(P0)) Pn = F(Pn-1)
![Page 4: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/4.jpg)
Introduction
• Process of Generation: Randomness • Statistical Self-Similarity • Different Generating Approaches
![Page 5: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/5.jpg)
Midpoint Subdivision (curve)
A
B
![Page 6: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/6.jpg)
Midpoint Subdivision (curve)
A
B C
M Issues Magnitude of MC Direction of MC
![Page 7: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/7.jpg)
Midpoint Subdivision (curve)
A
B
![Page 8: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/8.jpg)
Example
![Page 9: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/9.jpg)
Example
![Page 10: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/10.jpg)
Subdivision Methods (surface)
Triangle Edge subdivision
Iteration N
![Page 11: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/11.jpg)
Subdivision Methods
v
v
v
Iteration N+1
Triangle Edge subdivision
![Page 12: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/12.jpg)
Subdivision Methods
Triangle Edge subdivision
![Page 13: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/13.jpg)
Subdivision Methods
Triangle Edge subdivision Issues
Amount of displacement Direction of displacement “consistency”
![Page 14: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/14.jpg)
Subdivision Methods
Triangle Edge subdivision
![Page 15: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/15.jpg)
Example
![Page 16: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/16.jpg)
Subdivision Methods
Iteration N
Diamond Square subdivision
![Page 17: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/17.jpg)
Subdivision Methods
Diamond Square subdivision
Iteration N+1
![Page 18: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/18.jpg)
Subdivision Methods
Square Square subdivision
Iteration N
![Page 19: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/19.jpg)
Subdivision Methods
Iteration N+1
Square Square subdivision
9 3
3 1
Bilinear Interpolation
![Page 20: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/20.jpg)
Applications
• Coast Lines • Landscapes • Clouds • Candies • Stones • OTHERS
![Page 21: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/21.jpg)
Applications
• Coast Lines • Landscapes • Clouds • Candies • Stones • OTHERS
![Page 22: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/22.jpg)
Applications
• Coast Lines • Landscapes • Clouds • Candies • Stones • OTHERS
![Page 23: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/23.jpg)
Fractal Plants (L-Systems)
• Production rules applied to seed axioms. • Example
• Axiom B • Rule B->ABB
![Page 24: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/24.jpg)
Fractal Plants (L-Systems)
![Page 25: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/25.jpg)
Fractal Plants (L-Systems)
http://algorithmicbotany.org Prof. PrzemyslawPrusinkiewicz
![Page 26: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/26.jpg)
Mandelbrot’s Function
z z2 + c z and c are complex Algorithm
c : point in the region (x + iy) z0 : initial value of z zn = zn-1
2 + c Evaluate S(zn): if > Tolerance
assign color (n) to c If n > Limit
assign color (n) to c
![Page 27: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/27.jpg)
Mandelbrot’s Function
![Page 28: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/28.jpg)
General Formulation If the iteration function is z zα + c ; where α : integer or real, positive or negative
Then the number of complete lobe structures L = floor (abs(α - 1))
Fractional part of α is proportional to the size of an emerging baby Lobe.
![Page 29: Recapitulation - IIT Delhi](https://reader030.vdocument.in/reader030/viewer/2022032811/623ee174e76324339e1c2006/html5/thumbnails/29.jpg)
General Formulation