This is a web page with annotations for the code in the file shelling.c, which is a C program implementing Thomas Schelling's model of segregation from Micromotives and Macrobehavior, according to a Pascal version of that model written by Robert Axelrod. To download the C code without these remarks please follow this link:
There are three versions of this program, annotations for the other two are the files:
As with other C programs the file starts with #include statements, which instruct the compiler to import programming libraries that this program will need. What follows are definitions of constants, and declarations of global variables and function prototypes.
#include <stdio.h> #include <math.h> #include <stdlib.h> /* Schelling's model of segregation. C code by Benedikt Stefansson January 1998 based on original Pascal code by Tom Belding and Robert Axelrod */ /* Define constants */ #define number_of_reports 8 #define events_per_report 100 #define num_white 25 #define num_agents 50 /* Declare arrays */ static int occupant[64]; static int color[num_agents]; static int location[num_agents]; static int neighbor_loc[64][8]; /* Declare subroutines */ int content(int i); void random_move(int i); int get_random_location(); void initial_output(); void initialize_agent_color(); void initialize_agent_location(); void initialize_neighbor_list(); void periodic_output(int event,int moves);
The main function is the "main loop" of the program. It will set up the model according to the predefined parameters, and fill in the initial values for agents, such as color and location. Then it iterates through a two level loop, an outer loop which are the "time steps" and an inner loop which are the events within each time step. Each event consists of a function call to an agent, where it is determined whether the agent is satifsied or not, and if the agent is not happy in his neighborhood he finds a random empty location on the lattice and moves there.
void main() {
int i;
int report;
int events_in_report;
int event=0;
int moves_this_period=0;
/* Initialize lattice and neighborhood list */
initial_output();
initialize_agent_color();
initialize_agent_location();
initialize_neighbor_list();
periodic_output(0,0);
/* Count timesteps or events */
event = 0;
i = 0;
/* Outer event loop */
for (report=0;report<number_of_reports;report++) {
/* Count of actual moves */
moves_this_period = 0;
/* Inner event loop */
for (events_in_report = 0;events_in_report < events_per_report;events_in_report++) {
event++;
/* Work our way through the agent list */
if (i > num_agents)
i = 0;
if (!content(i)) {
/* If agent is not content then move it*/
moves_this_period++;
random_move(i);
}
i++;
}
/* Print out report */
periodic_output(event,moves_this_period);
}
exit(0);
}
The content function takes an integer argument and returns an integer value. If the return value is 0 the agent is unhappy and if it is 1 he is content. The integer argument refers to the ID number of the agent, this allows the function to look up his location and neighborhood by ID.
int content(int i) {
/* Calculate if agent i is content and
return 1 if he is and 0 if not */
int n;
int result;
int neighboor;
int address;
int neighborhood_cell;
int same_color_count=0;
int occupied_count=0;
address=location[i];
for(n=0;n<8;n++) {
/* Check if neighborhood cell is on map and occupied */
neighborhood_cell=neighbor_loc[address][n];
if(neighborhood_cell!=-1 && occupant[neighborhood_cell]!=-1) {
/* There is someone there */
occupied_count++;
/* But is he of the right color? */
if(color[occupant[neighborhood_cell]]==color[i])
same_color_count++;
}
}
/* Content if more than 1/3 of neighbors are same color */
if(same_color_count*3 > occupied_count)
result=1;
else
result=0;
return result;
}
The random_move function takes an integer argument and returns void (nothing). The argument is the ID number of an agent. The function calls a random number generating function through the get_random_location() function, until it finds an empty cell. It then proceeds to put the agent into the empty sell, and updating the information in the system accordingly.
The get_random_location() function takes no argument and returns an integer between 0 and the lattice size (which is hardcoded as being 64, i.e. 8 by 8). It accomplishes this by calling the rand() function, which returns an integer between 0 and RAND_MAX. We divide by RAND_MAX and thus get a floating point number between 0 and 1. Multiply this number by the size of the lattice and you get a number between 0 and the lattice_size. Note the casting between variable types, first from int to float and then back to int.
void random_move(int i) {
int trial_location;
int look=0;
/* Choose random locations until you
manage to find an empty one */
do{
trial_location=get_random_location();
} while(occupant[trial_location]!=-1);
/* OK - found empty location so move */
/* First remove agent at old location */
occupant[location[i]]=-1;
/* Then add him at the new location */
occupant[trial_location]=i;
/* Finally update location info for agent */
location[i]=trial_location;
}
int get_random_location() {
float p;
p=((float)rand()/(float)RAND_MAX);
return (int)(p*64.0);
}
The functions initialize_agent_color() and initialize_agent_location() select the color and initial location of agents at runtime. The first num_white agents are made white (0) and the rest non white (1).
void initialize_agent_color() {
/* Give each agent a color 0 or 1 */
int i;
for(i=0;i<num_agents;i++) {
if(i< num_white)
color[i]=0;
else
color[i]=1;
}
}
void initialize_agent_location() {
int i;
int trial_location;
for(i=0;i<64;i++) {
occupant[i]=-1;
}
for(i=0;i<num_agents;i++) {
do {
trial_location=get_random_location();
}while(occupant[trial_location]!=-1);
occupant[trial_location]=i;
location[i]=trial_location;
}
}
The function initialize_neighbor_list() fills in arrays with the location number of each of the 8 neighboring cells to each interior cell on the array - and the border cells which only have 5 neighbors. The calculation proceeds as follows: First calculate the default 8 cells for each of the 64 locations, then set the neighbors that are off the map to -1 which indicates that the location doesn't exist.
void initialize_neighbor_list() {
/* Precalculates Moore neighborhoods
for each location on map */
int l;
for (l = 0; l < 64; l++) {
/* First calculate general case */
neighbor_loc[l][0] = l - 9; /* NW */
neighbor_loc[l][1] = l - 8; /* N */
neighbor_loc[l][2] = l - 7; /* NE */
neighbor_loc[l][3] = l - 1; /* W */
neighbor_loc[l][4] = l + 1; /* E */
neighbor_loc[l][5] = l + 7; /* SW */
neighbor_loc[l][6] = l + 8; /* S */
neighbor_loc[l][7] = l + 9; /* SE */
/* Correct for top row */
if (l < 8) {
neighbor_loc[l][0] = 0;
neighbor_loc[l][1] = 0;
neighbor_loc[l][2] = 0;
}
/* Correct for bottom row */
if (l > 55) {
neighbor_loc[l][5] = -1;
neighbor_loc[l][6] = -1;
neighbor_loc[l][7] = -1;
}
/* Correct for right side */
if ((l % 7) == 0) {
neighbor_loc[l][2] = -1;
neighbor_loc[l][4] = -1;
neighbor_loc[l][7] = -1;
}
/* Correct for left side */
if ((l % 8) == 0) {
neighbor_loc[l][0] = -1;
neighbor_loc[l][3] = -1;
neighbor_loc[l][5] = -1;
}
}
}
Two functions to print a brief blurb at the beginning of a run, and then the periodic reports, which show the state of the lattice in terms of which agent occupies which cell and the color or each cell's occupant. The periodic_report() function is called after each events_per_period events.
void initial_output() {
/* Prints some information at beginning of run */
printf("Schelling's segregation model, coded by Benedikt Stefansson\n
based on Pascal program by by Robert Axelrod and Ted Belding\n");
printf("Parameters:\n");
printf(" Number of agents=%3d\n",num_agents);
printf(" Number of agents with color 0=%3d\n",num_white);
}
void periodic_output(int event,int moves) {
/* Prints out periodic state of map */
int line;
int address;
int column;
if(event==0)
printf("Initial state of map\n");
else
printf("Event %3d. Moves this period %3d\n",event,moves);
address=0;
for(line=0;line<8;line++) {
for(column=0;column<8;column++) {
/* Output agent map */
if(occupant[address]==-1)
printf(" . ");
else
printf("%3d",occupant[address]);
address++;
}
/* Rewind and put space between */
address-=8;
printf(" ");
for(column=0;column<8;column++) {
/* Output color map */
if(occupant[address]==-1)
printf(" . ");
else {
if(color[occupant[address]]==0)
printf(" @ ");
if(color[occupant[address]]==1)
printf(" # ");
}
address++;
}
printf("\n");
}
printf("\n");
}