/*
Fig (1)
Age distribution of a steady-state population: 
oldest cells appear with half frequency of youngest cells (exponential relationship)
Red line (median) divides population into two equal areas.


Fig (2) 
Cumulative plot, integration of (1) assuming population size=1, shows relation of rank vs age.
Rank is here a relative number  between 0 and 1. 
The equation allow to convert age into rank.
Example: when sorting, the median cell has rank = 0.5.
This corresponds to age = 0.415

Fig (3) 
This is the same as Fig 2 with x and y swapped. 
But also the equation solved for age.
Here, we can convert rank into age.


*/      

nPoints = 100;
ageX = 0.414;
close("*_");
xValues = newArray(nPoints);
yValues1 = newArray(nPoints);
yValues2 = newArray(nPoints);
yValues3 = newArray(nPoints);

for (p = 0; p < nPoints; p++) {
	age = p/nPoints;
	xValues[p] = age;
	freq = pow(2, -age);
	yValues1[p] = freq;
	yValues2[p] = 2-2* pow(2, -age);
	if(age < ageX){
		yValues3[p] = freq;
		last = p;
	}
	//age = log(1-0.5*rank)/log(0.5);

}
yValues3 = Array.trim(yValues3, last+1);

Plot.create("(1) Age distribution_", "Age", "(1) Frequency = 2^^-Age^^");
Plot.setFrameSize(400, 250 );
Plot.setColor( "#ddddff");
Plot.setLineWidth(3);
Plot.setColor("blue", "#eeeeff");
Plot.add("filled", xValues, yValues1);
Plot.setColor("blue", "#ddddff");
Plot.add("filled", xValues, yValues3);

Plot.setLineWidth(2);
Plot.setColor( "red");
Plot.drawLine(ageX, 0.75, ageX, 0);
Plot.drawGrid;
Plot.setLimits(0, 1, 0, 1);
Plot.setAxisLabelSize(18.0, "plain");
Plot.setFontSize(12.0);
Plot.show;


Plot.create("(2) Cumulative Plot_", "Age", "(2) Rank = 2-2*2^^-Age^^");
Plot.setFrameSize(400, 250 );
Plot.setColor( "#ddddff");
Plot.setLineWidth(3);
Plot.setColor("blue", "#eeeeff");
Plot.add("line", xValues, yValues2);
Plot.setLineWidth(2);
Plot.setColor( "red");
Plot.drawLine(ageX, 0.5, ageX, 0);
Plot.drawLine(0, 0.5, ageX, 0.5);
Plot.drawGrid;
Plot.setLimits(0, 1, 0, 1);
Plot.setAxisLabelSize(18.0, "plain");
Plot.setFontSize(12.0);
Plot.show;


Plot.create("(3) Cumulative Plot swapped_", "Rank", "(3) Age=log(1-0.5*rank)/log(0.5)");
Plot.setFrameSize(400, 250 );
Plot.setColor( "#ddddff");
Plot.setLineWidth(3);
Plot.setColor("blue", "#eeeeff");
Plot.add("line", yValues2, xValues);
Plot.setLineWidth(2);
Plot.setColor( "green");
Plot.drawLine(0, ageX, 0.5, ageX);
Plot.drawLine(0.5,  0, 0.5, ageX);
Plot.drawGrid;
Plot.setLimits(0, 1, 0, 1);
Plot.setAxisLabelSize(18.0, "plain");
Plot.setFontSize(12.0);
Plot.show;