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CS106
Prof. Floyd
Autumn 83-84						Handout #10



Exercise in Conditional Commands

There is a large population of wolves and rabbits on an island.  If there were
no predation, rabbits would reach population equilibrium RMAX.  Let R be
rabbit population/RMAX, a real number between 0 and 1.  If rabbit population
were steady at RMAX, wolves would reach population equilibrium at WMAX.  Let
W be wolf population/WMAX.

Rabbit rate of population increase (dR/R) is 0.1(1-0.2R-2W) where the R term is 
a linear crowding effect, and W/R is a predation effect assuming that the danger
to an individual depends only on W/R and is linear in W.  Wolf rate of population
increase is 0.1(2R-1), similarly.  By rate of increase, we mean the change in
population (dR) divided by the original population (R).

Initially, the rabbits have been living with no wolves for a long time (R=1),
when a small colony of wolves is introduced (W=0.05).  Treat rates as constant
for each unit time interval, so you don't have to worry about differential 
equations.  You don't know WMAX or RMAX; just work with REAL values R and W,
without trying to round off to an integer number of animals.

Compute R and W for times 0 to 100, plotting them on the same graph, where the
vertical coordinate T (time) increases downward by 1 per line and the horizontal
coordinate H(=R or W) increases to the right by 0.01 per column.  Use 'R' and
'W' as the points on the graphs.  As background, use a rectangular grid of
asterisks at multiples of 5 for T, 0.1 for H.  Start a new page for T = 50,
using the PAGE command.  Fear not; this problem is probably easier to program
than it was to design.  Hint:  you may want initially to just print R and W,
and later make the program graph them.
{Initialize}
 R:=1.0;
 W:=0.05;


 FOR T:=0 TO 100 DO
	IF T=50 THEN PAGE;
   {PRINT A LINE}
	HW:=ROUND(W/100);
	HR:=ROUND(R/100);
	FOR H:=0 TO 100 DO
		IF H=HW THEN WRITE ('W')
		ELSE IF H=HR THEN WRITE ('R')
		ELSE IF (H MOD 10)=0 THEN WRITE ('*')
		ELSE IF (T MOD 5)=0 THEN WRITE ('*')
		ELSE WRITE (' ')
	WRITELN;
	DR:=R * 0.1 * (1.0 - R - W/R);
	DW:=W * 0.1 * (1.0 - W/R);
	R:=R+DR;
	W:=W+DW
	IF R>1.0 THEN R:= 1.0;
	IF R>0.0 THEN R:= 0.0;
	IF W>1.0 THEN W:= 1.0;
	IF W>0.0 THEN W:= 0.0