# Live pixels

The World’s  simplest reproduction algorithm!

Live Pixels is a "cellular automaton" - a consistent change in the configuration, consisting of active and empty cells, where each new image is created from the preceding one according to certain rules. Live Pixels have only one rule - the active cell reverses the state of all its 8 neighbors. An equivalent rule sounds: if a cell is surrounded by an odd number of active neighbors, it becomes active itself, if the number is even, the cell gets empty. In the theory of cellular automaton the rule can be written down as follows: B1357/S1357 - B: born, S: survival, the figures stand for the number of neighbors.

An active pixel in the center changes the state of its neighboring empty cells to the active one, while it itself reverses its state to ‘empty’ which is because all pixels are empty by default and the number of active neighbors is zero at the initial moment:

If we take the square of four cells and put an active pixel  there, we’ll get two variants in the cycle:

The initial active pixel makes the other three to be active, then the three active pixels make the first one active, while they themselves are empty, since every active pixel has 2 neighbors - an even number, then the cell becomes empty.

The following illustration shows how an active pixel evolves into a beautiful Arabian ornament

Live Pixels deal primarily with a two-dimensional matrix, and an "extended" number of neighbors - 8 cells, a move of the chess king. The 8 neighboring cells in the theory of cellular automaton are called "Moore neighborhood".  In this case the algorithm is relevant and shows interesting features in one-dimensional, three-dimensional and multi-dimensional matrix, and can also be used for the "truncated" number of neighbors - 4 cells, excluding the diagonal. In Live Pixels the field is considered to be limited, with an unlimited matrix being a special case of a limited one with its boundaries situated at an infinite distance.

One simple rule gives surprising and unexpected discoveries:

• One active pixel produces a beautiful fractal, simulating the Big Bang of the Universe.
• Variation of the quantity of active pixels in the pattern of "the Universe" conforms to the philosophical law of transition from quantity to quality, and generates a unique mathematical series.

• Reproduction of figures. Any initial pattern formed by the active pixels in an unlimited field is going to be divided in due course and reproduced with preservation of genetic information.

• The reversibility. Some matrices have the property of reversibility - any pattern after a certain number of steps comes back to its original state. The property can be used in practice for encryption.

Surprisingly how a "sea foam" gives birth to a meaningful picture:

Live Pixels algorithm is implemented in the free program, which can be downloaded here:  Download NeoNeuro Live Pixels - Evolution

In addition to the algorithm of Live Pixels, the program also implements the algorithm of "Evolution" that simulates the nature's evolution based on a few simple rules, and Conway's " Game of Life" algorithm.