Introduction to the Modeling and Analysis of Complex Systems

13.5. SIMULATION OF CONTINUOUS FIELD MODELS 253* Dt/(2*Dh)- wy * config[x, (y-1)%n])\config, nextconfig = nextconfig, configimport pycxsimulatorpycxsimulator.GUI(stepSize = 50).start(func=[initialize, observe, update])In this example, we simulate the transport equation with (w x , w y ) = (0.01, 0.03) in a 2-D[0, 1] × [0, 1] space with periodic boundary conditions, starting from an initial configurationthat has a peak in the middle of the space:c(x, y, 0) = exp(− (x − )0.5)2 + (y − 0.5) 2(13.43)0.2 2The temporal and spatial resolutions are set to ∆t = 0.01 and ∆h = 0.01, respectively(so that the size of the grid is 100 × 100). This is a very slow simulation process, so thestepSize is set to 50 to skip unnecessary visualizations (see the last line). The surfaceplot is used to visualize the configuration in 3-D axes. Note that you need to call the showcommand at the end of the observe function, because changes made to 3-D axes arenot automatically reflected to the visualization (at least in the current implementation ofmatplotlib).The result of this simulation is shown in Fig. 13.13, where you can clearly see the peakbeing transported to a direction given by (w x , w y ). Moreover, thanks to the interactivenature of pycxsimulator.py, this 3-D visualization is now interactively manipulatable evenif you are not running it from Anaconda Spyder, Enthought Canopy, or other interactiveenvironments. You can click and drag on it to rotate the surface to observe its 3-D structurefrom various angles.If you don’t need a 3-D surface plot, you can use imshow instead. This makes the codea bit simpler, and yet the result can be as good as before (Fig. 13.14):Code 13.6: transport-ca-imshow.pyimport matplotlibmatplotlib.use(’TkAgg’)from pylab import *n = 100 # size of grid: n * nDh = 1. / n # spatial resolution, assuming space is [0,1] * [0,1]Dt = 0.01 # temporal resolution