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Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Exercise 9A (i) Consider the Hénon attractor from week 5. Generate a set of points in the attractor (say, 105 points) for parameter values a = 1.4, b = 0.3. (ii) Plot a graph of log N(e) against log(1/e) for sensibly chosen values of €, and by estimating its gradient, give an estimate of the fractal dimension of the Hénon attractor. The true box-counting dimension is 1.261 0.003. How close is your estimate? (iii) How could you make this estimate more accurate? (iv) Another interesting two-dimensional map which produces chaotic dynamics and a fractal attractor is the Ikeda map. This can be written xn+1=R+ C₂(xn costn Yn sin tn) Yn+1=C₂(xn sin tn + yn costn) C3 where tn C₁ 1+z2+². Taking parameters R = 1.0, c₁ = 0.4, c₂ = 0.9, c3 = 6.0, plot the Ikeda attractor and compute its box-counting dimension.
Transcribed Image Text:Exercise 9A (i) Consider the Hénon attractor from week 5. Generate a set of points in the attractor (say, 105 points) for parameter values a = 1.4, b = 0.3. (ii) Plot a graph of log N(e) against log(1/e) for sensibly chosen values of €, and by estimating its gradient, give an estimate of the fractal dimension of the Hénon attractor. The true box-counting dimension is 1.261 0.003. How close is your estimate? (iii) How could you make this estimate more accurate? (iv) Another interesting two-dimensional map which produces chaotic dynamics and a fractal attractor is the Ikeda map. This can be written xn+1=R+ C₂(xn costn Yn sin tn) Yn+1=C₂(xn sin tn + yn costn) C3 where tn C₁ 1+z2+². Taking parameters R = 1.0, c₁ = 0.4, c₂ = 0.9, c3 = 6.0, plot the Ikeda attractor and compute its box-counting dimension.
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