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.
A complex adaptive system is entity of networks and connections. It can “learn and adapt to change over time” which can change the “structure of the system” (Clancy, Effken, Pesut, 2008). It contains twelve elements: autopoesis or self-regenerization, open exchange, participation in networks, fractals, phase transition between order and chaos, search for fitness peaks, nonlinear dynamics, sensitive dependence, attractors that limit growth, strange attractors of emergence...
A Cellular Automata can be viewed as an autonomous Finite State Machine[FSM] consisting of a number of cells.
The development of the Chaos began with a computer and mathematic problems of random data that can calculate and predict patterns that repeat themselves. For example, it picks up the pattern of a person’s heart beat and the pattern of snowflakes hitting the ground. Researchers have found that the patterns may be viewed as “unstable”, “random” and “disorderly” they tend to mimic zig-zags, lightning bolts or electrical currents. This theory has not only been used by physicist, but has also been used by astronomers, mathematicians, biologists, and computer scientists. The Chaos Theory can be applied to predict air turbulence, weather and other underlying parts of nature that is not easily understood (Fiero, p.
The simulator does something similar to this. The organisms in the beginning are identical. They have arms of a similar length as a result of their phenotypes. To simulate nature, every cycle we could say represents a generation. Every generation we see new organisms born with random mutations. Based on the environment we see different mutations on the newborn. For example, if its environment through the generations allowed its ancestors to survive, based on the phenotypes we saw in the ancestors we can see them again in the newborn. Basically saying that the parents of the newborn lived long enough to mate with the same traits., in turn giving the newborn those same exact traits. In this case, it is traits which code for arms length.
Throughout the modern era scientists and mathematicians have believed the world and it’s various systems follow a linear order. Much like a clock ticking second by second, minute by minute, hour by hour, day by day. The belief was predictable in nature, following a simple order. However, there are many unexplainable events that occur every second across the world that do not fit this model. The opposite theory by natural law is chaos. Ancient Greek philosophers believed Chaos was evil, it dwelled in the underworld among the dead, it was opposite of Gaia, the goddess of the earth that was seen as good and orderly. In 1961 scientist began to study the idea that they may have missed something big and that was ideas of chaos and how it related to weather, science and especially ecology.
Pineda, R. G., Tjoeng, T.H., Vavasseur, C., Kidokoro, H., Neil, J.J., & Inder, T. (2013). Patterns
This is the 2nd classification of an assembly language. It was introduced in the late 1950’s. The 1st generation language being binary, i.e. combination of 1’s and 0’s was difficult to understand and there was high chances of error and hence the 2nd generation language was introduced. This language used letters of the alphabet instead of 1’s and 0’s making it easier to use. Some of its properties are:
Two billion years ago two prokaryotes bumped into each other and formed the first multi-cellular organism. 65 million years ago an asteroid hit the earth and dinosaurs became extinct. Three days ago, in your notebook, you drew a mess of squiggles which to you represented Jackson Pollock's painting, Number 1, 1948. You wrote the word entropy on the upper left hand corner of the page. On the bottom right hand side you wrote, Creativity is based on randomness and chance.
34 Rocha, L. M. 1998 : Selected Self-Organization and the Semiotics of Evolutionary Systems pp 6-7
Tank, David W. and John J. Hopfield. "Collective Computation in Neuronlike Circuits." Scientific American. 1987. PDF. 24 March 2014. .
This structure is formed through the biological process of growth, where neurons fire together, which
The prefix function Π for a pattern encapsulates knowledge about how the pattern matches against shifts of itself. This information can be used to avoid useless shifts of the pattern ‘p’. In other words, this enables avoiding backtracking on the string
This lead Lorenz to come up with the idea of how nature works, that “small changes can have large consequences”. It is later deemed the title of the “butterfly effect” after Lorenz suggested that a flap of a butterfly’s wings in Brazil could cause a tornado in Texas. The butterfly effect is also known as “sensitive dependence on initial conditions, the same idea that Poincaré proposed. In 1963, Lorenz wrote a paper, Deterministic Nonperiodic Flow, which included the butterfly effect. His acumen resulted as the foundation principle of the Chaos Theory, “which expanded rapidly during the 1970s and 1980s into fields as diverse as meteorology, geology, and biology” (Pacaud et al.). However, as the message was passed down the line, some of it got lost, and now Lorenz’s message is only about half alive.
Chaos theory has numerous application including helping explain phenomena or helping to predict the future. Chaos theory is applicable in various fields ranging from weather, business to medicine. Chaos theory explains the reason why it is practically improbable to predict the weather with the current technology as well as providing a way for people to find patterns in the chaotic system of stock exchange. It also helps with the running of organisation by showing what sort of condition is needed for a profitable business as well as helping doctors predict when heart failure may occur. Fractals which is a concept of chaos theory also is portrayed in the natural world in examples such as lightning and neurons in the brains. Chaos theory has
As the name suggest, one node becomes the master and all other are slaves. Master stores the whole population and evaluate the individuals of this population and send these individuals to different slaves for calculating the fitness or to apply the genetic operators over the individual of the population. Slaves receives the individuals calculate the fitness, and send results back to the master. This allows utilization of computing power of the different processors. And finally master node makes a selection for the optimal