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 <i>K</i> function, <i>K(t) = pi * t^2</i>, 
corresponding to a completely random pattern.
<p>

To decipher the different colours, look at the printed output 
when you plot the <i>K</i> function. For example:
<blockquote><kbd>
      data(cells)<br>
      plot(Kest(cells))
</kbd></blockquote>
gives the following output: 
<blockquote><kbd>
<table>
<tr>
 <td></td>
 <td>lty</td>
 <td>col</td>
</tr>
<tr>
  <td>iso</td>
  <td>1</td>
  <td>1</td>
</tr>
<tr>
  <td>trans</td>
  <td>2</td>
  <td>2</td>
</tr>
<tr>
  <td>border</td>
  <td>3</td>
  <td>3</td>
</tr>
<tr>
  <td>theo</td>
  <td>4</td>
  <td>4</td>
</tr>
</table>
</kbd></blockquote>
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).
<p>

To understand what the abbreviations `iso', `trans' and `border' 
mean, 
type something like this:
<blockquote><kbd>
           myK 
<- Kest(mydata)<br>
           myK
</kbd></blockquote>
Then the object <kbd>myK</kbd> contains the estimated K functions (all 
the different
estimates). When you type the name of the object <kbd>myK</kbd>, a lot of 
information is printed out. For example 
<blockquote><kbd>
     data(cells)<br>
     K <- Kest(cells)<br>
     K
</kbd></blockquote>
yields output like this:
<blockquote><kbd>
Function value object (class 'fv')<br>
for the function r -> K(r)<br>
Entries:<br> 
<table>
<tr><td>id</td><td>label</td><td>description</td></tr>
<tr><td>r</td>
    <td>r</td>
    <td>distance argument r</td>
</tr>
<tr><td>theo</td>
    <td>Kpois(r)</td>
    <td>theoretical Poisson K(r)</td>
</tr>
<tr><td>border</td>
    <td>Kbord(r)</td>
    <td>border-corrected estimate of K(r)</td>
</tr>
<tr><td>trans</td>
    <td>Ktrans(r)</td>
    <td>translation-corrected estimate of K(r)</td>
</tr>
<tr><td>iso</td>
    <td>Kiso(r)</td>
    <td>Ripley isotropic correction estimate of K(r)</td>
</tr>
</table>
</kbd></blockquote>

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.
<p>

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

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). 
<p>

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.
<p>

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. 
<p>

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