These curves are different estimates of the K function, using different `edge correction' techniques. Also one of the curves is the theoretical value of the K function, K(t) = pi * t^2, corresponding to a completely random pattern.

To decipher the different colours, look at the printed output when you plot the K function. For example:

data(cells)
plot(Kest(cells))
gives the following output:
 lty col iso 1 1 trans 2 2 border 3 3 theo 4 4
This means that the estimate of the K function by the `iso' method is plotted in solid lines (lty=1) in black (col=1), the estimate of the K function by the `trans' method is plotted in dashed red lines (lty=2, col=2) and so on. The last one called `theo' is the theoretical K function K(t) = pi * t^2, which is plotted in dotted blue lines (lty=4,col=4).

To understand what the abbreviations `iso', `trans' and `border' mean, type something like this:

myK <- Kest(mydata)
myK
Then the object myK contains the estimated K functions (all the different estimates). When you type the name of the object myK, a lot of information is printed out. For example
data(cells)
K <- Kest(cells)
K
yields output like this:
Function value object (class 'fv')
for the function r -> K(r)
Entries:
 id label description r r distance argument r theo Kpois(r) theoretical Poisson K(r) border Kbord(r) border-corrected estimate of K(r) trans Ktrans(r) translation-corrected estimate of K(r) iso Kiso(r) Ripley isotropic correction estimate of K(r)
This table reports that the curve labelled `iso' is the estimate of K(r) by Ripley's isotropic correction, and the curve labelled `border' is the border-corrected estimate of K(r), etc.

For further information about the different edge corrections, see help(Kest).

The estimates of K(r) by different techniques should be roughly equal. If the curves for `iso', `trans' and `border' are wildly different, this suggests that estimation of K is difficult for these data (e.g. because there are too few data points, or the window is too irregular).

The standard interpretation of the plots of the K function is that, if the estimated K function curve lies above the theoretical curve, then the pattern is clustered, while if the estimated K lies below the theoretical curve, then the pattern is regular.

The names of the different estimates (iso, trans, border etc) depend on which function you are estimating. So to understand the plot coming from Gest, Jest, Fest, consult the appropriate help files.

For information on how to modify the plot of the K functions, see help(plot.fv) or the examples in help(Kest).