Game of Life+. Englsh Version.

Overview of research areas. Else see 'Traler'.







The purpose of creation of the given site - demonstration of that new is made, specifically by the author, on a theme Game of Life, the intellectual game invented by John Horton Conway about 50 years ago. The game is known as Evolution according to first translation into Russian /1971/.


New Game - Life+, that is too chess Evolution, intellectual game for youth and students, working, scientific, pensioners... The chessboard, one - two complete sets of usual draughts is everything that is necessary for the Game!


Except stated, so Life+ in its various variants: colour and volume, helicoid and cyclotrons, chess and billiards on a chessboard is not dull leisure where new and not investigated, without exaggeration, meets continually, induces to expansion of the knowledge in various areas of a science...






Classification of Life+/Evolution by dimension and chromaticity signs, by directions and rules of transformations, in particular, to values of constants of evolution, in the sizes and activity of a game field, its geometry, by quantity of players, activity of game is carried out.


In a material are considered active, with direct algorithm of game on a plane, mainly black-and-white, on the limited inactive field, in rectangular system of co-ordinates, in its pair variants. Restriction of a game field is realised by a rule of reflexion from borders.


Two-color game. Predominance algorithm. Random seeding of colors in the geometry of Figure 'Eight'.
Color stabilization after 8 moves of transformations.








Activity of game is realised by a rule of introduction-deducing by players in the course of game of chips on a game field. In a black-and-white, chess variant the prepotent, dominant algorithm of transformations is used, cumulative purposes in new Game of Life+ are given.


The simplest example. Original figure >> 1-st generation after 'R-pentamino'.


Activ game. Introduced c3. Generation 1* >> 2.


Activ game. Deduced f4. Generation 2* >> 3. Final configuration - 4 'blocks'. Game over.







Algorithmic modification of the Game of Life. Volume Life+/Evolution. In material are considered three-dementional, dimensionality L3T, with direct algorithm of the transformations, as monochrome , so black-and-white (cheaa), in limited inactive volume, in rectangular system of co-ordinates, in mono- and pair variants of the Game.


3D monochrome Life+. Transforvations in volume the figure 'Cube 2x2x2'.

The Restriction of the playing volume is realized by procedures of the reflection or absorptions on its border. Activity or passivity of the game is realized by possibility of introduction - removing in process of the play chips in playing volume. Such Evolution is defined as volume, three-dementional in chess its variant. Happen to as computer, so desk realization.






Evolution-Life+ expansions on games in colour are offered: on algorithm of averaging of colour of again formed chip; on algorithm of superposition when the figure is represented consisting of three in the basic tones; on nominant algorithm when min and max colours in a generating triad are rejected, and colour of a birth defines the remained.


Full-color game. Algorithm of superposition monochrome images. Figure 'super П-pentamino'.


Symbol substitution full-color images. Classic superpositional algorithm of transformations.






Billiard systems of evolutin. Pattern movement in the channel is limited in the mirror or wadded image. Algorithm of transformations is orthogonal as providing pattern movement in the channel with certain speed and acceleration.


The length of the channel unlike the specified systems is commensurable with its width. Mirror or wadded borders conclude a pattern in an original trap, moving which on a game field with certain speed, in this or that direction it is necessary to deliver lost-free a pattern to a billiard pocket.


Feature of game is that that an actively developing pattern through open gate of a trap can seep in open space if parameters of its motion is selected inexact. Consequence of such infiltration is difficultly operated nuclear reaction of growth of a configuration.


Labirinth system of evolution. Moving the pattern through a given maze. Ortogonal algorithm.




Billiard system of evolution. The trap is located in the center. Ortogonal algorithm.






Helicoid and cyclotron systems of evolution. Helicoid systems is a representation in the form of a spiral, of the channel, of the narrow process of evolution limited from three parties. The channel of movement of a pattern is limited in the mirror or wadded image. Algorithm of transformations is mainly orthogonal as providing pattern movement in the channel with certain speed and acceleration.





Helicoid system of evolution. Spiral pattern movement. Ortogonal algorithm.




Cyclotron system of evolution. Circular pattern movement. Ortogonal algorithm.

Helicoid systems are presented by monochrome and the chess type, representing all civilisation or only the head of process, one or several (two) civilisations in their competitive development. A special case of the stated - cyclotrons Shch when pattern development occurs on a circle or an ellipse, on a cylinder surface, on Moebius's surface…






The problem of searching for of the predecessor forward given one-coloured figure Is stated. Offered heuristic and machine, on method Monte-Carlo ways of the decision of this problem. Happen to the concrete results. Stated is reduced to optimum, on shown here criterion to models of the development of the generations.


The problem of searching for of the predecessor is put in varicoloured and three-dementional variant of Evolution. Representation of the figures is realized by the rules chess and Excel notation.


Searching for of the predecessor 'R-pentamino'. Search result in the center. One-color variant.






Evolution expansions on games in colour are offered: on algorithm of averaging of colour of again formed chip; on algorithm of superposition when the figure is represented consisting of three in the basic tones; on nominant algorithm when min and max colours in a generating triad are rejected, and colour of a birth defines the remained.


Developed a card game that will impress fans of gambling. Fundamentally the game is divided into the game on the figure, and on color. Rules the game on the figure: set the original (see top) empty layout, for example, four-way glider cycle.


It is necessary to choose a card from the deck (see below) corresponding to the direct course of transformations - which is easy. Or back transformation which is much more difficult. Next you need to fill in the initial layout sequentially. The correct filling of the layout when playing on the figure is given (see middle).


Card game Life+. The original empty layout. The correct layout. Card deck.






As the special case of the previous is considered prepotent - dominant algorithm in a black-and-white variant of game when colour of a chip is defined on prevalence of colour in a generating triad. Except colour - volume algorithms are investigated, and the last are given in the formalized kind, and representations of figures are carried out by rules chess and Excel notations.


Simplest Super16 based on algorithms Life+. One-color (1-4) and two-color (5-7).
Ortogonal algorithm. Playing field 4x4. No reflection from borders.






Sound images of the Game are created on the basis of both direct display of situations on the playing field, so indirect - for the purposes of harmonious sound close to the musical.


Evolution suite in author notanion. See more on site the author.







In Addition - the Computer graphics and Practical applications. Some exhibits of the Game of Life/Evolution: logoes, abstract scenes, design of the works of art...


Computer graphics based on algorithms Game of Life+.







Here Evolution/Life+, unlike classical Life is a pair, active game on a chessboard! Except stated, so Life+ in its various variants: colour and volume, helicoid and cyclotrons, chess and billiards on a chessboard is not dull leisure where new and not investigated, without exaggeration, meets continually, induces to expansion of the knowledge in various areas of a science...


At the same time, the author concerns with the subject Alternative tourism in Russia, which is defined as by itself organized tourism of the non-standard notable places. One more direction occupation author - colour-geometric prospecting, which presents searching for of the additional expressive facilities of the poetical process. If there are adherents, interested persons - join!







New Life+/Evolution - game rules, examples, theory elements.
Play, experiment, write down courses, create the etudes, give favourite, develop practice, create the game theory!
Infinite quantity of the configurations subject to players! Fantastic riches of combinations on a chessboard!








Game of Life+. Trailer.


Gennady Shcheglov - engineer-mathematician, candidate of Sciences, associate Professor.

D. H. Conway Game of Life has been passionate about since 1971, after being published in the journal of Scientific American.

Along with the works in the field of mathematical modeling of technical and economic systems, at different times performed work on the topics of Life / Evolution.


This search predecessors, algorithmic extensions in the color and volume, for games in a limited space, their sonic images... Practically all directions are realized, beginning with Dnepr-21 computer in programming language INF, up to modern PCs.

This long-term hobby has led to
.the development, in addition to the above, paired, active, in half a limited space version of the game, that is, chess Evolution, so called by analogy with the famous game: two players, a chessboard, black and white figures, the rules of recording moves.

From the simplest Super15 to chess, color and volume, sound interpretations, cyclotrons, labirinths, all this made by the author on the subject of Life/Evolution. Fan leisure, where new, unexplored meets at every turn, encourages the expansion of knowledge in various fields of science, art, sport...








Playing field 64x64. The classical algorithm. Full-colour. Superposition.

Specify the scenarios:



0 and none - П-hexaminoes,
1 - R-pentamino,
2 - wick,
3 - superposition of П-hexamine,
4 - superposition of  B-hexamine,
5 - Space Ships flight. 

Attention for scenarios 0, 1, 2.


1. Seeding of color is made in the geometry of these figures.
2. Development is happening on classic laws Conway.
3. There are rules of color formation, see section Life+.
4. When the situation stabilizes, stop the process by pressing X in the browser bar.
5. Sowing of colors to geometry is unique, i.e. when the next address on the hyperlink  Play here! seeding not repeats itself!
6. Set scenario from the list above, for example, 3.


Scenarios 3, 4, 5 are offered with a sophisticated mind.







Playing field 20x20. The classical algorithm.
Seeding of color. Two-colour game.


Specify the version of scenarios


0 or none - eight, 1 - chain  Ц5,
2 - chain  Ц7,
3 - pentadecathlon,
4 - toggle switch,
5 - the collision of two gliders,
6 - too, four,
7 - the cross,
8 - chains,
9 - collision of two LWSS,
10 - too, MWSS,
11 - Г-hexamine,
12 - R-pentamino.


Attention.


1. Seeding of color is made in the geometry of these figures.
2. Development occurs according to the classic Conway.
3. There are rules of color formation.
4. If the situation stabilizes, stop the process by pressing X in the browser bar.
5. Sowing of colors to geometry is unique, i.e. when the next address on the hyperlink  seeding not repeats itself!
6. Set scenario from the list above, for example, 3.






Azart Game of Life+. Welcome!

Azart game on the basis of the Life+ . Here, after the 4th move, the balance of the chips is 5:5.


1. Gambling on the basis of the Life+ provide initial random seeding. See left.
2. After n steps of the development >> stop-playing. See right.
3. The difference in the number of chips sides x the price of the chips gives your win.
4. Games of this type - both on the chessboard and computer. 
5. The version with average risks is given.
6. Step-by-step control of Conway's transformations by means of chess notations.


Attention.

1. Primary random seeding  made in the 4x4 field in the center chessboard.
2. Random seeding  both the  geometry and the colors into this geometry are given.
3. Development is happening on classic laws Conway.
4. The rules of color formation   and reflection  from the borders of the playng  field are given.
5. The number of  transformation steps is set by the players in the query window.
6. With an equal number of chips of the parties, by agreement, take into account the color of the field  the  board.
7. At the death of the group - right diagram is empty, seeding is recommended to repeat.
8. Chess notations of initial and current positions are given for control.
9. Seeding figure   geometry and  the colors in this geometry are unique! 10.Step-by-step control of transformations is carried out by Continue button...





Rules the Game of Life. Classic.

Any Chip with fewer than two neighbours dies* (underpopulation).
Any Chip with two or three live neighbours lives* (next generation).
Any Chip with more than three neighbours dies* (overpopulation).
Any Empty Cell with exactly three neighbours becomes a Chip* (reproduction).

Rules the Game Life+. From the author.

Two-color game. The predominance of color in a generating triad.**
Full-color game. Decomposition and further superposition the monochrome images.**
Ortogonal (4 neighbors) vs. classic (8 neighbors) algorithm transformation.**
Rule a reflection (absorption) from borders of limited space.**
Rule an activity (or no) of the Game.**

* - Conway.
** - else see site.






About sources.

The fantastic combinations... game "life", Scientific American, № 4, 1970.
M.Gardner, Matematicheskie dosugi, Mir, 1972.
Magazine Nauka i Zhizn, N8, 1971; N8, 1972, etc...
Internet: visti.net/skl, beluch.ru, life.written.ru, michurin.net,.. sites and monography of the author, etc.

Chess Evolution /Lambert, 2012, p. 88/ [RUS].

Summery List.
Introduction.
Section I. Game rules and the elementary examples.
Section II. The passive beginnings and continuations.
Section III. The active beginnings and continuations.
Section IV. Stable configurations and the terminations.
Section V. Colour collisions and border formations.
Section VI. Other games.
Symbols.
The dictionary of terms.
Appendices.

See else at http://shcheglov.clan.su/index/lection/0-19






Keywords:


John Horton Conway
Game of Life
Life+
Evolution
Predominance algorithm
Ortogonal & classics
Superposition & decomposition
Chess ~ black & white
Full-color & two-color
Predecessor
Helicoid & cyclotron
Billiard & labirinth
Volume & 3D
Activ game
Azart game
Sound images
Graphics
Gennady Shcheglov












Let us translate into English together!

To be continued...


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Game of Life+. Englsh Version. Trailer.

Overview of research areas the auther. Rules of the Game.
Sources. Keywords.


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