Fig. 2. a) Example of vegetation patterns generated by the model in a numerical simulation on a square 500 x 500 grid. The parameters are β' = 0.9, γ' = 0.155, with random, uniformly distributed initial conditions for R (in [0.42, 0.57]) and V initially equal to 0. Seedling dispersal occurs at rate λ = 1.7 · 10^{3} pixel^{1} per unit time, with each seedling having initial biomass, V_{0} = 0.01. The kernel function, k, is different from zero (and positive) only in the eight nearest neighbors of each pixel, with k being a linearly decreasing function of the distance, and the sum of k calculated for each pixel and its nearest neighbors being equal to 1. The spatial coordinates are rescaled as x' = x √(α /D_{0}) and y' = y √(α /D_{0}). b) Aerial view (taken from Okin and Gillette (2001), Fig. 3c) of vegetation from the Jornada site, in the Chihuahuan Desert (New Mexico). c) Same as a) but with λ = 7 · 10^{3} pixel^{1} per unit time, and random initial conditions for R taken as uniformly distributed in [0.4, 0.5]. d) Satellite view of vegetation patterns from a shrubland, 30 miles southwest of Las Cruces, New Mexico (32° 12' 28'' Lat N; 106° 51' 15'' Long W). Images in Fig. 2b, d were converted from the original images to a grayscale raster format, and transformed into a binary matrix (using a threshold filter).
