Define C, L, 0, and I. Give the results for p=0.45 and p=1.0 that you have calculated for Figure 15.2.
\f> amu login - Bing X B Quizzes - EVSP627 1001 Fa X Landscape Patterns as Ind X Homework2.pdf X Microsoft Word - GridPap X + X https://myclassroom.apus.edu/shared/commonfolder/science-and-technology-common/EVSP/EVSP... Z 3 of 4 Q + A v v Percolation theory provides a framework for examining landscapes as two- and quantnying men mnci and outel cages. (AT one trustCT, Who QUIT cages ana dimensional grids, usually square grids of size mi X m containing in' unique 0 inner edges; (B) two clusters with a total of 10 outer edges and 0 inner edges: and sites or cells. Gardner in chapter 13 uses computers to create random two- (C) one cluster with 4 inner edges (not 7) and 16 outside edges (not 7). dimensional maps of various sizes ranging from 50 x 50 to 500 x 500 cells. Here, you will use pencil and papers to generate smaller 10 X 10 grids containing 100 unique sites or cells. To be sure that you understand how to count clusters and outer and inner Consider the probability, p. that any of the 100 cells is occupied by a edges, consider the following example (Fig. 15.2), where p = 0.45. (Answers particular habitat type (c.g., forest or grassland). In an empty (homoge- are at the end of this portion of the exercise.) neous) 10 X 10 grid, p = 0. If you choose two random coordinates (x,y) and What is C? fill in that cell on the grid, then p = 0.01. If p = 0.10, then 10 cells are - L? - 0?- occupied; when p = 1.0, all 100 cells are occupied. When the grid contains To further check your understanding, consider a completely filled grid (p = some cells of the habitat of interest, several properties about its spatial 1.0): arrangement can be measured. For example, we can measure the number of habitat patches or clusters, their sizes, and the amount of edge surrounding What is C"? L? 0? -0+1- the habitat patches. On our hypothetical 10 X 10 landscape where p = 0.01, Look back at Figure 15.2, where p = 0.45, and note that although the grid we observe: is almost half full, it is not possible to "travel" from one edge of the grid to C = number of clusters = 1 the other edge on occupied (filled) clusters. (Remember that a diagonal L = size of largest cluster = 1 cell does not connect clusters; travel across a diagonal is disallowed). When the O = number of outer edges = 4 habitat is not connected, we say that the grid does not percolate. From 1 = number of inner edges = 0 percolation theory, we know that on a random map with the rules defined In this exercise, the following definitions and rules for describing the above, habitat will suddenly become connected at p = 0.5928 (Stauffer spatial patterns will be followed. These calculations are illustrated for the 1985). This value is called the critical threshold for percolation, or p. In the simple maps shown in Figure 15.1. exercise explained below, students should begin to watch for percolation at approximately p = 0.50. 1. An edge is a surface of an occupied cluster adjacent to an unoccupied area. 2. Outer edges fie along the outside of a cluster. 3. In contrast, inner edges are adjacent to unoccupied areas completely enclosed by a cluster, like the holes in Swiss cheese. 4. Two clusters only merge into one when they share an horizontal or vertical edge; a diagonal does not connect clusters. 5. When it falls on the edges of the grid, the outside-most edge of the patch should always be included in your count of outside edges, but not for your count of inside edges. Type here to search O L 9 J 3:13 PM Rain... 11/27/2021
