The tree and forest structure of "∧" growing bases obtained had made the foundation of computer modeling on random Koch curve island. Three kinds of random Koch curve islands were defined. It was analysed that stable fractal dimension of the second and the third kinds of the above islands could be obtained only from the perimeter area relation. The compute programe modeling the above islands and their fractal dimension was provided. From compute results

it was cleared that how the islands was selected and the number of island pairs needed in determining of fractal dimension and statistical dimension. The results also showed that both the relation ship between fractal dimension (or statistical dimension) and nesteed tier

and the relationship between distributions of regression straight lines of lgP—lgA from three kinds of the islands and nested tier.