CELL-MOSAIC AUTOMATA MODEL DESCRIPTION OF PETROLOGIC TEXTURAL TRANSFORMATIONS 

Cell-mosaic automata model helps to formulate all those descriptions we do in practice when we analyse for example the texture of a rock in thin section. We imagine the steps of formation of the texture and the sequence of these discrete changes in a cell-mosaic system is formulated on two hierarchy levels: on cellular one (minerals), and on global one (texture itself). The cell-automata mosaic's flow-chart has a framework of description: it is composed from two parts. The first one gives the structure and initial conditions of the cellular background, the second one gives the transitional functions. Both parts form a pair of approach: a local and a global one, as follows (Fig. 1.) The advantages of the cell-automata mosaic model come from this separability of local and global picture: both for conditions and operations, and from the expressed connections (feedback possibility) between the local and global characteristics. (We made such style of descriptions of sequence of crystallization of 70017 high Ti basalt texture, a metamorphic sequence of terrestrial textures, Grossman type CAI condensational sequence (this last one was almost in this form and carbonaceous chondritic aqeous alteration sequence, in one of our papers sent to the NASA LPSC 30 conference). 

CELLULAR AUTOMATIC FRAMEWORK 

The two times two definition structure of the cellular automaton model is a characteristical framework. The first block gives the structure of the cellular background, the second one gives the transitional functions. Both parts of conditions form a pair of approach: a local and a global one, as follows: 

A. CELLULAR BACKGROUND 
Aa. Local characteristics of the cell-mosaic system give the form of cells, their connections and neighbourhood relations. Ab. Global characteristics of the cell-mosaic system give the surface and the enclosure of the local relations to form a whole. 

B. TRANSITIONAL FUNCTIONS 
Ba. Local transitional function for cell mosaic elements which are individual automata (discrete function in space and time, step by step transforming cell-states) Bb. Global transitional function for the whole surface populated by the cell-mosaic system (it forms a sequence of stages of the surface taken step by step, as a consequence of summerized - for all cells - local transitional functions.) Although the points a and b are not independent of each other, the advantages of the cellular automaton model come from this separability of local and global picture: both for conditions and operations, and from the expressed connections between the local and global characteristics of the phenomenon. 

  a. LOCAL (CELL-LEVEL) b. GLOBAL (TEXTURAL)  
A. CELLULAR BACKGROUND Aa. Local characteristics of the cell-mosaic system give the cells, as actors in events, the form of the cells, their connections (i.e. faces) and neighbourhood relations.  Ab. Global characteristics of the cell-mosaic system give the texture and the sum up of the local relations. (i.e. the texture is a piokilitic type, because of enclosing relations) 
B. TRANSITIONAL FUNCTIONS Ba. Local transitional function for cell mosaic elements which are individual automata (discrete function in space and time, step by step transforming cell-states, i.e. how distinct minerals change) Bb. Global transitional function for the whole surface populated by the cell-mosaic system (sequence of stages of the texture taken step by step, as a consequence of summed up (for all cells) of the local transitional functions.) 

THE INDIRECT WAY OF CONSTRUCTION OF CELLULAR AUTOMATON MODEL: THE INDIRECT VON-NEUMANN PROBLEM 

The classical way of the development of a cellular automaton model was the construction of Aa and Ab background and the Ba local transitional function, at first. Then followed the deduction of the global transitional function Bb, which hold the primary goal of the construction. We may call this way of model construction to the direct way. (The principal aim of von Neumann s cellular automaton construction was to build a self-reproducing structure on the level of global transitional functions.) Our way of construction in this paper is the indirect way in respect of von Neumann s direction of construction (von Neumann, 1966.). After streching the background by the determination of points of Aa and Ab we formulate Bb global transitional function as a sequence of stages of discrete steps of transformations of the cell-mosaic system: and finally we construct the Ba local transitional function for the cells themselves. In the recent paper the global transitional function has two steps and three stages of state. We introduce to symbol them as follows: V-#-R (V-for cut, #-for motions, R-for glue parts together). But before cellular automaton model development we show the problem in a classical way. 

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Fig.1. The Transformations by its Phases principle

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Fig. 2. The decomposition of the Whole, which has symmetries. a. The symbol shows, that elements build up the whole. b. The symbol shows the two hierarchy levels of the whole; used later

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Fig. 3. The Whole with symmetry and so with two hierarchy levels has been substituted into the graph of the Transformations by its Phases principle (Fig. 1.) in the form of b. of Fig. 2.

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Fig. 4. Separation of phase blocks to its two parts gives the most characteristical framework of the cellular automatic description: the two parallel „equarions of motion”: that on the higher level of hierarchy – i.e. the Global Transitional Function, and that on the lower level of hierarchy – i.e. the Local Transitional Function. Both functions are discrete functions in time.