Chapter 13 - Davidson Physics

CHAPTER 14. FRACTALS AND KINETIC GROWTH MODELS 5340.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 00.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 10.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 20.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 30.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 40.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 50.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 60.55 0.22 0.61 0.34 0.720.70 0.13 0.04 0.89 0.590.10 0.07 0.84 0.42 0.64t = 7Figure 14.9: Example of a cluster formed by invasion percolation on a 5 × 3 lattice. The lattice att = 0 shows the random numbers that have been assigned to the sites. The darkly shaded sites areoccupied by the invader that occupies the perimeter site (lightly shaded) with the smallest randomnumber. The cluster continues to grow until a site in the right-most column is occupied.Two search methods are provided for determining the position of a new perimeter site inthe perimeter lists. In a linear search we go through the list in order until the random numberassociated with the new perimeter site is between two random numbers in the list. In a binarysearch we divide the list in two, and determine in which half the new random number belongs.