A critical factor affecting real ecosystems is the fragmentation of species habitats. Very few theoretical studies (not to speak about empirical ones) have been performed, however, to reveal the impacts of fragmentation in a rigorous quantitative way. Our extended Daisyworld model allows for such investigations with special emphasis on the modification of habitat geometry. Within the framework of our tutorial model we can expect, in particular, that fragmentation will create ``ecological niches'' for plants of inferior fitness and obstruct the forage activities of the animals.
Before we describe our specific way of fragmenting the landscape, let us mention that the 2D model without herbivores and homogeneous habitat exhibits an even better self-stabilizing ability than the simple LWM. However if the environmental stress - increasing insolation, for instance - exceeds a certain critical threshold, ``life'' breaks down on the artificial planet via first-order phase transitions. The latter fact implies the presence of hysteresis effects including bistability. A detailed account of those findings is given in von Bloh[5].
Here we focus on the modifications of geosphere-biosphere dynamics as triggered by restricting the habitable zone within our model world. In order to be specific, we generate landscape heterogeneity by employing the well-known percolation model from solid state physics [6].
The percolation model on a square lattice is formulated in the following way:
For a given probability 
, each site will be randomly occupied with
probability p. As a consequence, it will remain empty with probability 1-p.
A connected group of occupied sites is called a ``cluster''. The size of the
clusters clearly grows with increasing p. ``Percolation'' is said to set in
when the largest cluster extends from one end of the system to the other
(``spanning cluster''). In the limit of infinitely large lattices there exists a sharp
threshold value 
for percolation. The spanning cluster
associated with this phase transition is a multiple-connected fractal object
with a power-law hole-size distribution. Fig. 1 gives an example of such a critical
configuration which allows to traverse the entire lattice via next-neighbour
steps.
Figure 1: Patchwork of occupied sites in the standard percolation model
at criticality 
. The fractal spanning cluster is indicated
in black.
Therefore, we have to distinguish between three qualitatively different regimes determined by the occupation probability:
: the collection of occupied sites does not form any
spanning cluster, but the collection of unoccupied sites represents a connected
``void space''.
: neither the occupied nor the void sites form a
connected structure.
: the collection of occupied sites does form a connected
structure, but the void space is now disconnected .
We introduce civilisatory land-use into our extended Daisyworld by gradually
diminishing the potential growth area in the following way: choose a (small)
generating probability 
. In the first time step, consider all cells
within the finite lattice one by one and exclude them from the growth space
with probability . At time 
, the probability that any specific site
has been ``civilized'' is therefore given by
On the other hand, the statistical fraction of habitable area after n time
steps can be calculated by
Note that, our fragmentation scheme is independent of the actual status of the cell under consideration and all physical properties, such as diffusive heat transport remain unaffected.