Ergodic Behavior of Geomorphic Landforms

In geomorphology, there are several discussions from theoretical approach and among these subjects; it can be emphasized on morphogenesis succession and its modeling in that subject. In different categories the course of ergodicity is one of the most important subjects. This filed which has been adopted of physical thermodynamic science also in geomorphology is under study. Simply the importance of this subject is referred to historical modeling, because one of the most imperative phenomena in biologic, geologic, and also geomorphologic fields is time and its relationship with changes and successions. Phenomena in astronomical time are not appropriate for description, while there is not suitable time substitution in their relation. Ergodicity theorem was stated in physics for the first time and then formulated by mathematics. Ergodic hypothesis in which observation on a member of an ensemble during the time is the same as the average of the ensemble at definite time was became from 1960 became as analogy in experimental sciences. At first in biology as allometry and then in chemistry and geology it attracted the scientists and gradually influenced in geomorphology by some idioms like geographical cycle and unifomitarianism. Some of geomorphology researchers around the world attempted to interpret this theorem quantitatively. However, in Iran there is a little consideraction on it and this paper is trying to explain the dimensions of ergodicity. Its analog face in geomorphology provides a background to start the quantitative researches in Iran. The relationship between evolution, repetition, palimpsest, waves, the origin of phenomena and fractal geometry with ergodicity are subjects that have been considered in this research. After explanation of physical dimension and ergodic mathematical equations, and ergodic evolution of gullies at Khoor-Biabanak district we studied its accuracy whit an emphasis on it. It is obvious, with attention to this fact that the subject is very new, a broad opportunity is resulted which causes the ergodic literature in geomorphology to become enriched.