Multiple invasion percolation

We generalize the standard site invasion percolation model to permit simultaneous invasion of several sites. We propose two kinds of generalizations: one in which the invasion flux is controlled by the perimeter size and another where the growth process is commanded by the scaling properties. The acceptance profile as well as the fractal dimensions DF are carefully studied. For the model based on scaling relations, DF can be treated as a mere real parameter in the range (0, infinity). In the intervals (0, 91/48) and (2, infinity) the system is frustrated. For DF > 2 the model exhibits also an interesting burst phenomenon which is explained in the text. In the region [91/48, 2], the clusters obey exactly and in any scale the relations M similar to Rg(DF) between the mass M and the gyration radius Rg. These stabilized random fractals may be very useful in the study of dilute systems.