1 Introduction

  Mandelbrot mentioned [6] one of the curiosities of fractal terrains: fractal terrains look like fractal terrains even when you turn them upside down. Statistical parameters are equal in both cases. This property is typical for geologically new landscapes in nature. Moreover; the fractal techniques [4, 6, 9], provide only visual approximation of real terrains.

This is almost never the case in nature, where depressions in the landscape fill up with all manners of detriment. This causes the landscape to be smoother over the ages of geologic time. Terrain is maggeted by water, attrited by particles of sand and dust flown in the wind, and crannied from influence of temperature amplitudes. Moreover; most of the terrains are also influenced by human factors. Majority of the natural influences are reflected as a kind of erosion. This problem has been addressed e.g. in [4, 5, 8, 9]. Mandelbrot also pointed out in 1988 [9, pages 243-260,]: "The most basic defect of fractal landscapes - the fact that this landscapes do not include the river network". The rivers represent another kind of erosion in the same way as rain, wind, temperature, and time. Lately, this problem has been addressed for instance in [5, 11].

Considering the criterion of terrain erosion, techniques for generation of eroded terrain models can be divided into two classes. The first class of algorithms generates already eroded terrains [4, 5, 9, 10, 11]. The second group describes erosion of any terrains [8], regardless whether the data representing the terrain was obtained with some artificial technique or real data was used.

Most frequently terrain model is defined as height field. Regular height field is defined as two dimensional array of altitude values where the distance between rows and columns is constant.

This paper is organized as follows: first we give review of the basic algorithms of generating fractal terrains; random midpoint displacement and spectral synthesis. The two classes of eroded terrains generation follow in the next section. This paper ends with approach based on rewriting of matrices.

Ivo Marak - marak@sgi.felk.cvut.cz