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Life-like cellular automaton

A cellular automaton is Life-like if it meets the following criteria: The array of cells of the automaton has two dimensions. Each cell of the automaton has two states. In each time step of the automaton, the new state of a cell can be expressed as a function of the number of adjacent cells that are in the alive state and of the cell's own state; this class of cellular automata is named for the Game of Life, the most famous cellular automaton, which meets all of these criteria. Many different terms are used to describe this class, it is common to refer to it as the "Life family" or to use phrases like "similar to Life". There are three standard notations for describing these rules, that are similar to each other but incompatible. Wolfram & Packard use the Wolfram code, a decimal number the binary representation of which has bits that correspond to each possible number of neighbors and state of a cell; the other two notations unpack the same sequence of bits into a string of characters, more read by a human.

In the notation used by Mirek's Cellebration, a rule is written as a string x/y where each of x and y is a sequence of distinct digits from 0 to 8, in numerical order. The presence of a digit d in the x string means that a live cell with d live neighbors survives into the next generation of the pattern, the presence of d in the y string means that a dead cell with d live neighbors becomes alive in the next generation. For instance, in this notation, Conway's Game of Life is denoted 23/3. In the notation used by the Golly open-source cellular automaton package and in the RLE format for storing cellular automaton patterns, a rule is written in the form By/Sx where x and y are the same as in the MCell notation. Thus, in this notation, Conway's Game of Life is denoted B3/S23; the "B" in this format stands for "birth" and the "S" stands for "survival". There are 218 = 262,144 possible Life-like rules, only a small fraction of which have been studied in any detail. In the descriptions below, all rules are specified in Golly/RLE format.

Several more rules are listed and described in the MCell rule list and by Eppstein, including some rules with B0 in which the background of the field of cells alternates between live and dead at each step. Any automaton of the above form that contains the element B1 will always be explosive for any finite pattern: at any step, consider the cell that has minimum x-coordinate among cells that are on, among such cells the one with minimum y-coordinate; the cell must have one neighbor, will become on in the next step. The pattern must grow at each step in each of the four diagonal directions. Thus, any nonempty starting pattern leads to explosive growth. Any automaton of the above form that does not include any of B0, B1, B2 or B3 cannot support movement or expansion of patterns because any cell outside a rectangular building box containing the pattern has at most three on neighbours. Most finite patterns in rules whose notation begins with B2, all finite patterns in rules beginning with B1, grow in all directions rather than remaining of bounded size, with a front that moves at the speed of light.

Thus, the remaining "interesting" rules are the ones beginning with B3 or beginning with B0. There are other cellular automata which are inspired by the Game of Life, but which do not fit the definition of “life-like” given in this article, because their neighborhoods are larger than the Moore neighborhood, or they are defined on three-dimensional lattices, or they use a different lattice topology. For example: Non-totalistic rules depend on the configuration of live cells in the neighborhood. Non-isotropic rules that behave differently in different directions. There are 2512 ≈ 1.34 * 10154 rules including isotropic rules. Isotropic non-totalistic rules behave identically under reflection. There are 2102 ≈ 5.07 * 1030 rules including outer-totalistic rules. Larger than Life is a family of cellular automata studied by Kellie Michele Evans, they have large radius neighborhoods, but perform “birth/death” thresholding similar to Conway’s life. These automata have eerily organic “glider” and “blinker” structures.

RealLife is the “continuum limit” of Evan’s Larger Than Life CA, in the limit as the neighborhood radius goes to infinity, while the lattice spacing goes to zero. Technically, they are not cellular automata at all, because the underlying “space” is the continuous Euclidean plane R2, not the discrete lattice Z2, they have been studied by Marcus Pivato. Carter Bays has proposed a variety of generalizations of the Game of Life to three-dimensional CA defined on Z3. Bays has studied two-dimensional life-like CA with triangular or hexagonal neighborhoods. Eppstein, Gliders in Life-Like Cellular Automata. Griffeath, David, "Totalistic Growth Rules with Moore Neighborhood", The Primordial Soup Kitchen, Department of Mathematics, University of Wisconsin. Game of Life - Conway and Variants - Online Software Tool

Tongogara Refugee Camp

Tongogara Refugee Camp is a refugee camp located near Chipinge, about 420 km southeast of Harare. It was established in 1984 after Zimbabwe had become independent from Great Britain, took in refugees from Mozambique who were fleeing from the war between the government and the Mozambican National Resistance Movement, it is estimated that as many as 58,000 refugees had occupied the camp in 1994. After 1995, many of its members returned to Mozambique, the camp closed. In 2017, the population of the camp was about 10,000; the camp has been supported by United Nations High Commissioner for Refugees for housing and clothing, by United Nations World Food Program for money and food, UNICEF for hygiene and sanitation, other organizations such as Terre des hommes in Italy for health care and education. Geographical coordinates -20.349785, 32.309918. In the early 1990s, it was estimated about 60,000 people resided at the camp. In 2007, the populace was about 2,673. In 2010, about 3,200 people were housed at the camp.

In 2017, it was estimated that about 8,982 of the 10,563 refugees to Zimbabwe have resided at the camp, with 6,713 from Democratic Republic of Congo, 842 from Mozambique. Other countries include Burundi, Somalia, Ivory Coast, Ethiopia, Sudan, Syria and South Africa. Tongogara Primary School was established within the camp, in 2017, the school had 1,694 students, it is home to a secondary school. Tongogara Primary School is a primary school in the Tongogara Refugee Camp in Zimbabwe; the school is situated 18 km along the dusty road. It is one of the few schools to have a bigger captivity of more than 5km in the resettlement areas of Hoyuyu in Mutoko District; the other neighbouring schools are Kushinga Secondary and Primary School and Nzira Secondary and Primary School. This school was opened in 1970 when local residence placed a complaint to the Mutoko District council for being too relaxed in building more schools in Hoyuyu. Children as far as 15km were struggling to travel the long distances to nearby Jekwa Primary and Secondary school.

As of 2017, the school had about 1,700 students. It is suffering from a significant shortage of both teachers and supplies; the school educate students up to the seventh grade and is a registered ZIMSEC primary examination center having more than 200 students siting for seventh grade final exams each year. The school consist of 14 blocks each having 4 classrooms. 1 of these blocks is used as Science laboratories for chemical and biology lessons. The other room is used as a computer laboratory; the school has a well developed sport infrastructure, an artificial football pitch, basketball court, tennis court, swimming pool, volleyball court etc. The school won 3 consecutive achievements from 2016 for the best infrastructure development in Mutoko District. Tongogara Refugee Camp report in 2007 as posted to The Daily Telegraph by WikiLeaks

Werrington County, New South Wales

Werrington County is a suburb of Sydney, in the state of New South Wales, Australia. It is 50 kilometres west of the Sydney central business district, in the local government area of the City of Penrith and is part of the Greater Western Sydney region; the suburb is residential with a high proportion of individual separate dwellings. Werrington County is part of the Indigenous Australian, Darug nation and is located in the Deerubbin Local Aboriginal Land Council Area Prior to European settlement, what is now Werrington County was home to the Mulgoa people who spoke the Darug language, as part of the Darug Nation, they lived a hunter-gatherer lifestyle governed by traditional laws, which had their origins in the Dreamtime. Their homes were bark huts called'gunyahs', they hunted kangaroos and emus for meat, gathered yams and other native plants. Shortly after the arrival of the First Fleet in Australia in 1788, an outbreak of smallpox decimated the local indigenous communities and made it easier for settlers to dispossess them of their land.

In 1806, Werrington County was established as part of a land grant to Mary King, the youngest daughter of Governor Philip Gidley King. Werrington County was farm land until the early 1980s when land lots were sold for the residential and commercial buildings in the present day suburb. Werrington County is geographically at a higher altitude than most other suburbs in the Penrith area. Werrington Creek runs on the eastern border of the suburb. Werrington Lakes lies on the southwestern corner of the suburb. Werrington County is home to a Child Care centre, Werrington County Shopping Village, Caltex and 7- Eleven Petrol stations, The Henry Sports Club, Namatjira Neighbourhood Centre, Golf and other sporting facilities; the suburb is within a few minutes drive to St Marys Shopping Centre located in St Marys, New South Wales which hosts over 40 retailers including Woolworths and Target. As per the 2016 Census there were 3,645 residents in Werrington County with an average weekly household income of $1,605 compared to the national average of $1,234.

50.2% were males and 49.8% were females. The median age was 36 years. 81.2% of people were born in Australia. The top other countries of birth were England 4.1%, New Zealand 1.4%, Scotland 1.2%, Ireland 0.7% and Philippines 0.6%. The most common ancestries were Australian 32.3%, English 28.2%, Irish 8.4%, Scottish 6.1%, Aboriginal and/or Torres Strait Islander 4.7% and German 2.5%. The top responses for religious affiliation were Catholic 35.8%, Anglican 27.1%, No Religion 16.0%, Presbyterian and Reformed 3.2% and Uniting Church 2.7%. The majority of people only spoke English at home with the other languages spoken being Spanish 0.8%, Greek 0.6%, Arabic 0.6%, Hindi 0.5% and Italian 0.5%. Werrington County Public School is located in John Batman Avenue; the primary school was established in 1982. The school was opened in 1993 and enjoys a fine reputation within the Penrith District; the nearest High School is Cambridge Park High School in Cambridge New South Wales. Werrington County has 5 parks covering nearly 29% of the total area which include Shaw Park, Ellison Reserve and Werrington Lakes Flora & Fauna Reserve.

The nearest Hospital is Nepean Hospital in Penrith. Werrington County has a Medical centre at the Werrington County Shopping Village. Werrington County has quick and easy access to Penrith by travelling west on Dunheved Road or along Great Western Highway; the suburb is serviced by the Great Western Highway and is in close proximity to the M4 Western Motorway which can be accessed via Kent Road for residents travelling towards the Sydney CBD. The nearest railway station is Werrington railway station on the T1 Western Line which provides direct train services to the Sydney CBD. Busways provides 3 services around the Werrington County area. Route 780 travels along Dunheved Road past the Werrington County Shopping Village before travelling to either Penrith or Ropes Crossing while Route 782 travels around Greenbank Drive and Henry Lawson Avenue before travelling to either Penrith or Werrington railway station. Route 785 travels via Cambridge Park to Werrington railway station covering parts of Werrington County.

At a local government level, Werrington County is part of the north ward of Penrith City Council, represented by Ross Fowler. At the state level, it is part of the Electoral district of Londonderry, represented by Labor Party member Prue Car. Federally, it is part of the Division of Lindsay, represented by Labor Party member Emma Husar. Werrington County is located in the Deerubbin Local Aboriginal Land Council Area

Anatoly Samoilenko

Anatoly Mykhailovych Samoilenko is a Ukrainian mathematician, an Academician of the National Academy of Sciences of Ukraine, the Director of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Anatoly Samoilenko was born in 1938 in the village of Radomyshl district, Zhytomyr region. In 1955, he entered the Geologic Department at the Shevchenko Kyiv State University. However, the extraordinary gift of Samoilenko for mathematics determined his destiny in its own way, instead of a known geologist, science got a prominent mathematician. In 1960, Samoilenko graduated from the Department of Mechanics and Mathematics at the Shevchenko Kyiv State University with mathematics specialization. At the same time, his first scientific works were published. In 1963, after the graduation from the postgraduate courses at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, Samoilenko defended his candidate-degree thesis "Application of Asymptotic Methods to the Investigation of Nonlinear Differential Equations with Irregular Right-Hand Side" and began his work at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR under the supervision of Academician Yu. A. Mitropolskiy.

In few years of diligent research work, Samoilenko became one of the leading experts in the qualitative theory of differential equations. In 1967, based on the results of his research in the theory of multifrequency oscillations, he defended his doctoral-degree thesis "Some Problems of the Theory of Periodic and Quasiperiodic Systems", the official opponents of which were V. I. Arnold and D. V. Anosov. In 1965–1974, Samoilenko worked as a senior research fellow at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR and gave lectures at the Shevchenko Kyiv State University. In 1974, he obtained the professor degree. In 1978, he was elected to become a Corresponding Member of the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, his monograph brought him worldwide recognition. This monograph was written by Samoilenko together with his teachers, Academicians N. N. Bogolyubov and Mitropolskiy. Thirty six years Samoilenko reminisced, "In Kyiv, at the Institute of Mathematics, great scientists were my teachers...

In many fields of science, they were'trendsetters' on the scale of the Soviet Union. It is important for a young scientist to belong to a serious scientific school. Only in this case he has a chance to obtain results at the world level; the atmosphere of a good scientific school itself stimulates a young scientist to carry out his research work at the cutting edge of modern science. And if he opens a new direction in science his name gains recognition". In 1974–1987, Samoilenko headed the Chair of Integral and Differential Equations of the Department of Mechanics and Mathematics at the Shevchenko Kyiv State University; these years were marked by high scientific activity of the chair. Based on results of the research in the theory of differential equations with delay performed at that time, the monograph of Mitropolskiy, D. I. Martynyuk was published. At the same time, together with his disciple M. O. Perestyuk, published the well-known monograph devoted to the theory of impulsive differential equations.

These monographs are cited in scientific literature. Since 1987, Samoilenko has headed the Department of Ordinary Differential Equations at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, since 1988 he has been the Director of the Institute of Mathematics of the National Academy of Sciences of Ukraine; the beginning of this fruitful creative period was marked by the fundamental monograph devoted to the qualitative theory of invariant manifolds of dynamical systems. This monograph served as a foundation for the construction of the general perturbation theory of invariant tori of nonlinear dynamical systems on a torus; the English version of this monograph is well known. Three years the monograph of Samoilenko was published. In this monograph, in particular, the method of Lyapunov functions was used for the investigation of dichotomies in linear differential systems of the general form; the results of many-year investigations of constructive methods in the theory of boundary-valued problems for ordinary differential equations carried out by Samoilenko together with M. Ronto are presented in monographs.

Constructive algorithms for finding solutions of boundary-value problems with different classes of multipoint boundary conditions were developed by Samoilenko, V. M. Laptyns'kyi, K. Kenzhebaev. Complex classes of resonance boundary-value problems whose linear pan cannot be described by Fredholm operators of index zero were investigated by Samoilenko, together with O. A. Boichuk and V. F. Zhuravlev, in monographs; the monograph of Samoilenko and Yu. V. Teplins'kyi is devoted to the theory of countable systems of ordinary differential equations; the monographs of Samoilenko and R. I. Petryshyn cover a broad class of qualitative problems in the theory of nonlinear dynamical systems on a torus. At present, Samoilenko is the author of about 400 scientific works, including 30 monographs and 15 textbooks, most of which have been translated into foreign languages, his monographs made an important contribution to mathematical education. According to MathSciNet, t

Timeline of the history of Tuvalu

This time line of the history of Tuvalu chronologically lists important events occurring within the present political boundaries of the Pacific island state of Tuvalu. This time line is introduced by the theories as to the origins of the Polynesian people and the migration across the Pacific Ocean to create Polynesia, which includes the islands of Tuvalu; the first inhabitants of Tuvalu were Americans so that the origins of the people of Tuvalu are addressed in the theories regarding the spread of humans out of Southeast Asia, from Taiwan, via Melanesia and across the Pacific islands to create Polynesia. There is evidence for a dual genetic origin of Pacific Islanders in Asia and Melanesia, which results from an analysis of Y chromosome and mitochondrial DNA markers), and archaeological evidence. There is evidence that Fiji playing a pivotal role in west-to-east expansion within Polynesia. In the archaeological record there are well-defined traces of this expansion which allow the path it took to be followed and dated with some certainty.

It is thought that by 1400 BC, "Lapita Peoples", so-named after their pottery tradition, appeared in the Bismarck Archipelago of northwest Melanesia. This culture is seen as having adapted and evolved through time and space since its emergence "Out of Taiwan". Within a mere three or four centuries between about 1300 and 900 BC, the Lapita archaeological culture spread 6,000 km further to the east from the Bismarck Archipelago, until it reached as far as Fiji and Samoa; the area of Tonga and Samoa served as a gateway into the rest of the Pacific region known as Polynesia. During pre-European-contact times there was frequent canoe voyaging between the islands as Polynesian navigation skills are recognised to have allowed deliberate journeys on double-hull sailing canoes or outrigger canoes. Eight of the nine islands of Tuvalu were inhabited; the pattern of settlement, believed to have occurred is that the Polynesians spread out from the Samoan Islands into the Tuvaluan atolls, with Tuvalu providing a stepping stone to migration into the Polynesian Outlier communities in Melanesia and Micronesia.

Tuvaluan mythology as to their ancestors is recounted in stories. On Niutao the understanding is that their ancestors came from Samoa in the 13th century. On Funafuti and Vaitupu the founding ancestor is described as being from Samoa. Tuvalu is thought to have been visited by Tongans in the mid-13th century and was within Tonga's sphere of influence; the extent of influence of the Tuʻi Tonga line of Tongan kings and the existence of the Tuʻi Tonga Empire which originated in the 10th century, is disputed. The oral history of Niutao recalls that in the 15th century Tongan warriors were defeated in a battle on the reef of Niutao. Tongan warriors invaded Niutao in the 15th century and again were repelled. A third and fourth invasion of Tongan occurred in the late 16th century, again with the Tongans being defeated. Tuvalu is on the western boundary of the Polynesian Triangle so that the northern islands of Tuvalu Nui, have links to Micronesians from Kiribati; the oral history of Niutao recalls that during the 17th century warriors invaded from the islands of Kiribati on two occasions and were defeated in battles fought on the reef.

HistoryTuvalu: A History Isala and Larcy, Institute of Pacific Studies, University of the South Pacific and Government of Tuvalu Pulekai A. Sogivalu, Brief History of Niutao, A, Published by the Institute of Pacific Studies. ISBN 982020058X Macdonald, Cinderellas of the Empire: towards a history of Kiribati and Tuvalu, Institute of Pacific Studies, University of the South Pacific, Fiji. ISBN 982-02-0335-X References