BTW Sandpile

Here is my little sandpile model. I am trying to teach myself a bit about self organized criticality, so I coded this up.

Well, here is the code!

Note: I edited this post because I found a small bug in the original code.

#! /Library/Frameworks/Python.framework/Versions/Current/bin/python


# I ripped off the mencoder stuff from thee matplotlib website
# That stuff is copyright Josh Lifton 2004, used with permission
# The rest is copyright J. Emrys Landivar 2010
#
# 'Permission is hereby granted to use and abuse this document
# so long as proper attribution is given.'


import numpy as np
import matplotlib.cm as cm
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
import matplotlib.colorbar as cbar
from numpy.random import randn
from scipy import integrate
import matplotlib
matplotlib.use('Agg')
import subprocess                 # For issuing commands to the OS.
import os
import sys                        # For determining the Python version.



table_size=31 #the size of the table that the sandpile is on
z_crit=4  #the critical size of a stack of grains, it will fall if there are more grains that that
num_grains=1000 #how many grains to drop
z=np.zeros((table_size+2,table_size+2)) #thisis the sandpile and the table it rests on
add_location=(table_size/2+1,table_size/2+1) # sets the middle of the table to drop grains on

#
print 'Executing on', os.uname()
print 'Python version', sys.version
print 'matplotlib version', matplotlib.__version__

not_found_msg = """
The mencoder command was not found;
mencoder is used by this script to make an avi file from a set of pngs.
"""  #this was shamelessly ripped off from elsewhere

try:
    subprocess.check_call(['mencoder'])
except subprocess.CalledProcessError:
    print "mencoder command was found"
    pass # mencoder is found, but returns non-zero exit as expected
    # This is a quick and dirty check; it leaves some spurious output
    # for the user to puzzle over.
except OSError:
    print not_found_msg
    sys.exit("quitting\n")



z2=z.copy()
fig=plt.figure()


for g in xrange(num_grains):
    z[add_location[0],add_location[1]] += 1 #drop a grain
    for x in xrange(1,table_size+1): 
        for y in xrange(1,table_size+1):
            if z2[x,y] > z_crit:  #check for colapse
                    z[x,y]-=4   #colapse
                    z[x+1,y]+=1
                    z[x-1,y]+=1
                    z[x,y+1]+=1
                    z[x,y-1]+=1
    z2=z.copy()
    
    #drop the grains over the edge off the table.
    z[0,0:table_size+2]=np.zeros(table_size+2)
    z[0:table_size+2,table_size+1]=np.zeros(table_size+2)
    z[0:table_size+2,0]=np.zeros(table_size+2)
    z[table_size+1,0:table_size+2]=np.zeros(table_size+2)
    
    #plotting!!
    ax=fig.add_subplot(111)
    ax.set_title('Height of the Sandpile')
    cax = ax.imshow(z, interpolation='nearest')
    cax.set_clim(vmin=0, vmax=8)
    cbar = fig.colorbar(cax, ticks=[0,3, 5, 8], orientation='vertical')

    filename = str('%03d' % g) + '.png'
    plt.savefig(filename, dpi=100)
    print 'Wrote file', filename
    
    plt.clf()

#print sum(sum(z))

#make the movie

command = ('mencoder',
            'mf://*.png',
            '-mf',
            'type=png:w=800:h=600:fps=25',
            '-ovc',
            'lavc',
            '-lavcopts',
            'vcodec=mpeg4',
            '-oac',
            'copy',
            '-o',
            'output.avi')

#os.spawnvp(os.P_WAIT, 'mencoder', command)

print "\n\nabout to execute:\n%s\n\n" % ' '.join(command)
subprocess.check_call(command)

print "\n\n The movie was written to 'output.avi'"

print "\n\n You may want to delete *.png now.\n\n"

Recalculation in the Manufacturing Labor Market

A new NY times story about how manufacturing jobs are having difficulty hiring people because of a skills shortage.  


Some random thoughts:

• This seems to me to be a failure of education.
• Eventually companies in the US will have to increase and fund their own education efforts (beyond just specific skills training), because it seems that our k-12 educational establishment has failed to teach a significant portion of our labor force.
• This all fits Arnold Kling's "recalculation" story.