This section discusses patterns formed by the evolution of cellular automata from simple seeds. The seeds consist of single nonzero sites, or small regions containing a few nonzero sites, in a background of zero sites. The growth of cellular automata from such initial conditions should provide models for a variety of physical and other phenomena. One example is crystal growth. The cellular automaton lattice corresponds to the crystal lattice, with nonzero sites representing the presence of atoms or regions of the crystal. Different cellular automaton rules are found to yield both faceted (regular) and dendritic (snowflake-like) crystal structures. In other systems the seed may correspond to a small initial disturbance, which grows with time to produce a complicated structure. Such a phenomenon presumably occurs when fluid turbulence develops downstream from an obstruction or orifice. (3)

Figure 2 shows some typical examples of patterns generated by the evolution of two-dimensional cellular automata from initial states containing a single nonzero site. In each case, the sequence of two-dimensional patterns formed is shown as a succession of ``frames.'' A space-time ``section'' is also shown, giving the evolution of the center horizontal line in the two-dimensional lattice with time. Figure 3 shows a view of the complete three-dimensional structures generated. Figure 4 gives some examples of space-time sections generated by typical one-dimensional cellular automata.

Examples of classes of patterns generated by evolution of two-dimensional cellular automata from a single-site seed. Each part corresponds to a different cellular automaton rule. All the rules shown are both rotation and reflection symmetric. For each rule, a sequence of frames shows the two-dimensional configurations generated by the cellular automaton evolution after the indicated number of time steps. Black squares represent sites with value 1; white squares sites with value 0. On the left is a space-time section showing the time evolution of the center horizontal line of sites in the two-dimensional lattice. Successive lines correspond to successive time steps. The cellular automaton rules shown are five-neighbor square outer totalistic, with codes (a) 1022, (b) 510, (c) 374, (d) 614 (sum modulo 2 rule), (e) 174, (f) 494.

With some cellular automaton rules, simple seeds always die out, leaving the null configuration, in which all sites have value zero. With other rules, all or part of the initial seed may remain invariant with time, yielding a fixed pattern, independent of time. With many cellular automaton rules, however, a growing pattern is produced.

Figure 2 shows some typical examples of patterns generated by the evolution of two-dimensional cellular automata from initial states containing a single nonzero site. In each case, the sequence of two-dimensional patterns formed is shown as a succession of ``frames.'' A space-time ``section'' is also shown, giving the evolution of the center horizontal line in the two-dimensional lattice with time. Figure 3 shows a view of the complete three-dimensional structures generated. Figure 4 gives some examples of space-time sections generated by typical one-dimensional cellular automata.

Examples of classes of patterns generated by evolution of two-dimensional cellular automata from a single-site seed. Each part corresponds to a different cellular automaton rule. All the rules shown are both rotation and reflection symmetric. For each rule, a sequence of frames shows the two-dimensional configurations generated by the cellular automaton evolution after the indicated number of time steps. Black squares represent sites with value 1; white squares sites with value 0. On the left is a space-time section showing the time evolution of the center horizontal line of sites in the two-dimensional lattice. Successive lines correspond to successive time steps. The cellular automaton rules shown are five-neighbor square outer totalistic, with codes (a) 1022, (b) 510, (c) 374, (d) 614 (sum modulo 2 rule), (e) 174, (f) 494.

With some cellular automaton rules, simple seeds always die out, leaving the null configuration, in which all sites have value zero. With other rules, all or part of the initial seed may remain invariant with time, yielding a fixed pattern, independent of time. With many cellular automaton rules, however, a growing pattern is produced.

Related

- Satisfactory Essays
## Cellular Automata Essay

- 1130 Words
- 3 Pages

Classification Wolfram,defined four classes into which cellular automata and several other simple computational models can be divided depending on their behavior.In order of complexity, the classes are:- • Class I CAs evolve4 to a uniform conﬁguration of cell states, from nearly any initial conﬁguration. This state can be thought of in dynamical systems terms as a ‘point attractor’, or ‘limit point’. As one would suspect, the rules for class I CAs map from most or all possible neighbour conﬁgurations to the same new state. Initial lattice conﬁgurations do exist for some class I CAs that lead to non-trivial cycles, but these are very rare. • CAs in Class II evolve to pro... ... middle of paper ... ...hborhood, additive CA are ideally suited for V LSI implementation.

- 1130 Words
- 3 Pages

Satisfactory Essays - Better Essays
## Comparing Mitosis and Meiosis

- 1215 Words
- 3 Pages

This is cell division; two types of cell division are Meiosis and Mitosis. The comparison will be between Meiosis 1 and Mitosis, because Meiosis 2 is much the same as Mitosis. Dividing cells have a regular pattern of events, known as the cell cycle. This cycle may be divided into two basic parts; The Interphase and the actual division (Meiosis / Mitosis). Interphase is when the cell is not dividing but duplicating its DNA and organelles.

- 1215 Words
- 3 Pages

Better Essays - Good Essays
## Difference Between Mitosis And Mitosis

- 1100 Words
- 3 Pages

The first sub phase of this is prophase 1 and this is split up into 5 stages. The first one is leptotene and this is where the chromosomes supercoil. The second one is zygotene and this is where the homologous chromosomes form pairs and these are called bivalents. Pachytene is where crossing over occurs between the homologous chromosomes and chiasmata form. Diplotene is where they start to separate but remain attached to each other by the chiasmata.

- 1100 Words
- 3 Pages

Good Essays - Powerful Essays
## Cellular Reproduction

- 2640 Words
- 6 Pages
- 5 Works Cited

In the first and longest phase of mitosis, prophase, the chromosomes become visible and the centrioles split in half and then move to opposite sides of th... ... middle of paper ... ...on’t seperate correctly. This is called nondisjunction. There are three types of nondisjunction, Trisomy- when a gamete with an extra chromosome is fertiized with a normal gamete. Monosomy- when a gamete with one chromosome is missing and is then fertilized by normal gamete. And Trioloidy- where both zygotes have an extra chromosome.

- 2640 Words
- 6 Pages
- 5 Works Cited

Powerful Essays - Good Essays
## Identification and Characterizaation of Three GS Isoforms

- 1027 Words
- 3 Pages

In this study we have attempted the characterization of the multiple GS cDNAs present. The characteristics details of the full-length cDNAs of GS01 (Accession No. JQ740737), GS02 (Accession No. JQ740738) and GS03 (Accession No. JX457351) are given in Table 2.

- 1027 Words
- 3 Pages

Good Essays - Powerful Essays
## Simple Evolution of Complex Crystal Sequences

- 1874 Words
- 4 Pages

Section~ ef{CellularAutomataSection} describes the cellular automata-based framework which we use to think about sets of DNA tile ribbon crystals and Section~ ef{CACrystalFitness} we describe how to predict the fitness of ribbon crystals of this type in our model. In Sections~ ef{IrreversibleAutomata}~and~ ef{ReversibleAutomata} we analyze the fitness landscapes of the sets of DNA tile ribbon crystals. We then use stochastic kinetic models of DNA tile ribbon assembly to simulate one kind of crystal evolution in Section~ ef{SimulationSection} and show that the outcomes of these simulations are consistent with the predictions made using our simpler model. Finally we conclude with some remarks about simple crystal evolution and its significance.

- 1874 Words
- 4 Pages

Powerful Essays - Better Essays
## Biology- Cell Division

- 1393 Words
- 3 Pages
- 8 Works Cited

Chromosome cohesion in mitosis and meiosis. Journal of Cell Science,120, 367-369. Karp, G. (1999). Cell and molecular biology concepts and experiments (2nd ed.). America, A: John Wiley & Sons, Inc. McIntosh, J. R., & McDonald, K. L. (1989).

- 1393 Words
- 3 Pages
- 8 Works Cited

Better Essays - Satisfactory Essays
## Matrix For Matrix Multiplication

- 638 Words
- 2 Pages

What is Systolic Architecture? A systolic array comprises of matrix like rows of data processing units called cells. Each cell gives the information to its neighbouring cell instantly after processing. The array is usually rectangular where data flows across the array between neighbouring cells, usually with different data moving in different directions. Systolic algorithm might be designed for matrix multiplication which is fed in one row at a time from the top of the array and is passed down the array.

- 638 Words
- 2 Pages

Satisfactory Essays - Good Essays
## Path Selection Method

- 933 Words
- 2 Pages

Next, a n'×n' matrix, M, is generated where the (i,j)th element of M is a tuple which its first item is j and its second item is the correlation between ith and jth paths (Cij). Hence, the ith row of this matrix shows the correlation of ith path with all other paths in U'. Note that -1 is considered as the value of Cii. Therefore, the matrix M will be M=[■((1,-1)&…&(n^',C_(1,n^' ))@⋮&⋮&⋮@(n^',C_(n^',1))&…&(n^',-1))] (1) Next, each row of the matrix is sorted separately based on the value of Cij of tuples from the high to low. After sorting, the tuples which cont... ... middle of paper ... ...in this work, based on our experiments, we consider a weight for (6) which is two times larger than the weight which is considered for (3), and also, consider a weight for (3) which is two times larger than the weight which is considered for (4).

- 933 Words
- 2 Pages

Good Essays - Powerful Essays
## History Of Reversible Logic

- 858 Words
- 2 Pages

2.6.2 Logic Function In classical computing, logic operations are defined as functions over Boolean variables B ϵ {0, 1}. Definition 2.1. A multi-output Boolean function is a mapping f : Bn → Bm, where B = {0, 1} is a Boolean domain and n, m ϵ N. In fact, it is a system of m Boolean functions fi ( x1, x2,....... xn ), where 1 ≤ i ≤ m. Such function can be expressed in

- 858 Words
- 2 Pages

Powerful Essays