A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
70-430: In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution , the frequency of different outcomes over repeated events (or "trials")
140-491: A simple random sample , is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. A random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where
210-538: A chosen effect on the viewer. Nature provides examples of many kinds of pattern, including symmetries , trees and other structures with a fractal dimension, spirals , meanders , waves , foams , tilings , cracks and stripes. Symmetry is widespread in living things. Animals that move usually have bilateral or mirror symmetry as this favours movement. Plants often have radial or rotational symmetry , as do many flowers, as well as animals which are largely static as adults, such as sea anemones . Fivefold symmetry
280-716: A clinical intervention is used to reduce bias in controlled trials (e.g., randomized controlled trials ). Religion : Although not intended to be random, various forms of divination such as cleromancy see what appears to be a random event as a means for a divine being to communicate their will (see also Free will and Determinism for more). It is generally accepted that there exist three mechanisms responsible for (apparently) random behavior in systems: The many applications of randomness have led to many different methods for generating random data. These methods may vary as to how unpredictable or statistically random they are, and how quickly they can generate random numbers. Before
350-538: A cyclical fashion." Numbers like pi are also considered likely to be normal : Pi certainly seems to behave this way. In the first six billion decimal places of pi, each of the digits from 0 through 9 shows up about six hundred million times. Yet such results, conceivably accidental, do not prove normality even in base 10, much less normality in other number bases. In statistics, randomness is commonly used to create simple random samples . This allows surveys of completely random groups of people to provide realistic data that
420-427: A die was released, a complete row of tokens (so, one citizen from each of the tribes of Athens) was either selected if the die was coloured one colour, or discarded if it was the alternate colour. This process continued until the requisite number of citizens was selected. Prior to 403 BCE, the courts published a schedule and the number of dikastes required for the day. Those citizens who wanted to be dikastes queued at
490-510: A medium – air or water, making it oscillate as they pass by. Wind waves are surface waves that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of dunes . Foams obey Plateau's laws , which require films to be smooth and continuous, and to have a constant average curvature . Foam and bubble patterns occur widely in nature, for example in radiolarians , sponge spicules , and
560-553: A mixture of these, such as the tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman. Quantum nonlocality has been used to certify the presence of genuine or strong form of randomness in a given string of numbers. Popular perceptions of randomness are frequently mistaken, and are often based on fallacious reasoning or intuitions. This argument is, "In a random selection of numbers, since all numbers eventually appear, those that have not come up yet are 'due', and thus more likely to come up soon." This logic
630-432: A population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, say research subjects, has the same probability of being chosen, then we can say the selection process is random. According to Ramsey theory , pure randomness (in the sense of there being no discernible pattern)
700-411: A roughly pyramidal form, where elements of the pattern repeat in a fractal -like way at different sizes. Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns. Gravity
770-476: A weighted lottery to order teams in its draft. Mathematics : Random numbers are also employed where their use is mathematically important, such as sampling for opinion polls and for statistical sampling in quality control systems. Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms . Medicine : Random allocation of
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#1732844802087840-587: A ‘global fractal forest.’ The local ‘tree-seed’ patterns, global configuration of tree-seed locations, and overall resulting ‘global-forest’ patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay
910-473: Is a source of ubiquitous scientific patterns or patterns of observation. The sun rising and falling pattern each day results from the rotation of the earth while in orbit around the sun. Likewise, the moon's path through the sky is due to its orbit of the earth. These examples, while perhaps trivial, are examples of the "unreasonable effectiveness of mathematics" which obtain due to the differential equations whose application within physics function to describe
980-404: Is approximated by randomization , such as selecting jurors and military draft lotteries. Games : Random numbers were first investigated in the context of gambling , and many randomizing devices, such as dice , shuffling playing cards , and roulette wheels, were first developed for use in gambling. The ability to produce random numbers fairly is vital to electronic gambling, and, as such,
1050-536: Is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity ‘global-forest’ patterns consisting of ‘tree-seed’ components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing. Kleroterion A kleroterion ( Ancient Greek : κληρωτήριον , romanized : klērōtērion )
1120-494: Is found in the echinoderms , including starfish , sea urchins , and sea lilies . Among non-living things, snowflakes have striking sixfold symmetry : each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms. Crystals have a highly specific set of possible crystal symmetries ; they can be cubic or octahedral , but cannot have fivefold symmetry (unlike quasicrystals ). Spiral patterns are found in
1190-410: Is impossible, especially for large structures. Mathematician Theodore Motzkin suggested that "while disorder is more probable in general, complete disorder is impossible". Misunderstanding this can lead to numerous conspiracy theories . Cristian S. Calude stated that "given the impossibility of true randomness, the effort is directed towards studying degrees of randomness". It can be proven that there
1260-511: Is infinite hierarchy (in terms of quality or strength) of forms of randomness. In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate. Beyond religion and games of chance , randomness has been attested for sortition since at least ancient Athenian democracy in
1330-559: Is only correct if applied to a system where numbers that come up are removed from the system, such as when playing cards are drawn and not returned to the deck. In this case, once a jack is removed from the deck, the next draw is less likely to be a jack and more likely to be some other card. However, if the jack is returned to the deck, and the deck is thoroughly reshuffled, a jack is as likely to be drawn as any other card. The same applies in any other process where objects are selected independently, and none are removed after each event, such as
1400-532: Is opposed to that component of its variation that is causally attributable to the source, the signal. In terms of the development of random networks, for communication randomness rests on the two simple assumptions of Paul Erdős and Alfréd Rényi , who said that there were a fixed number of nodes and this number remained fixed for the life of the network, and that all nodes were equal and linked randomly to each other. The random walk hypothesis considers that asset prices in an organized market evolve at random, in
1470-464: Is predictable. For example, when throwing two dice , the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability , and information entropy . The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there
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#17328448020871540-458: Is random if and only if it withstands all recursively enumerable null sets. The other notions of random sequences include, among others, recursive randomness and Schnorr randomness, which are based on recursively computable martingales. It was shown by Yongge Wang that these randomness notions are generally different. Randomness occurs in numbers such as log(2) and pi . The decimal digits of pi constitute an infinite sequence and "never repeat in
1610-415: Is reflective of the population. Common methods of doing this include drawing names out of a hat or using a random digit chart (a large table of random digits). In information science, irrelevant or meaningless data is considered noise. Noise consists of numerous transient disturbances, with a statistically randomized time distribution. In communication theory , randomness in a signal is called "noise", and
1680-566: Is some 'objective' probability distribution. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space . This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences . A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions . These and other constructs are extremely useful in probability theory and
1750-480: Is that a string of bits is random if and only if it is shorter than any computer program that can produce that string ( Kolmogorov randomness ), which means that random strings are those that cannot be compressed . Pioneers of this field include Andrey Kolmogorov and his student Per Martin-Löf , Ray Solomonoff , and Gregory Chaitin . For the notion of infinite sequence, mathematicians generally accept Per Martin-Löf 's semi-eponymous definition: An infinite sequence
1820-409: Is the result of previous events, as is reflected in the concept of karma . As such, this conception is at odds with the idea of randomness, and any reconciliation between both of them would require an explanation. In some religious contexts, procedures that are commonly perceived as randomizers are used for divination. Cleromancy uses the casting of bones or dice to reveal what is seen as the will of
1890-404: Is thought that it will occur less often in the future. A number may be assumed to be blessed because it has occurred more often than others in the past, and so it is thought likely to come up more often in the future. This logic is valid only if the randomisation might be biased, for example if a die is suspected to be loaded then its failure to roll enough sixes would be evidence of that loading. If
1960-499: The Monty Hall problem , a game show scenario in which a car is hidden behind one of three doors, and two goats are hidden as booby prizes behind the others. Once the contestant has chosen a door, the host opens one of the remaining doors to reveal a goat, eliminating that door as an option. With only two doors left (one with the car, the other with another goat), the player must decide to either keep their decision, or to switch and select
2030-471: The deterministic ideas of some religions, such as those where the universe is created by an omniscient deity who is aware of all past and future events. If the universe is regarded to have a purpose, then randomness can be seen as impossible. This is one of the rationales for religious opposition to evolution , which states that non-random selection is applied to the results of random genetic variation. Hindu and Buddhist philosophies state that any event
2100-429: The kleroterion and drew them one by one. If the die was white, the top row was selected as jurors. If the die was black, the archon moved on to the next row down from the top and repeated the process until all juror positions were filled for the day. The first significant examination of Athenian allotment procedures was James Wycliffe Headlam 's Election by Lot , first published in 1891. Aristotle's Constitution of
2170-512: The Athenians , the text of which was first discovered in 1879 and first published as Aristotle's in 1890, became an important resource for scholars. Throughout the text, Aristotle makes references to a lottery system which was used to appoint government officials. Archaeologists first discovered kleroteria in the 1930s in the Athenian Agora, dating them to the second century BC. In Aristotle,
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2240-501: The Kleroteria, and the Courts (1939), Sterling Dow gave an overview and analysis of the discovered machines. Contrary to previous scholars, who translated kleroterion as "allotment room," Dow reasoned that kleroterion cannot be translated to mean "room," as Aristotle writes: "There are five kanomides in each of the kleroteria . Whenever he puts in the kyboi, the archon draws lots for
2310-406: The advent of computational random number generators , generating large amounts of sufficiently random numbers (which is important in statistics) required a lot of work. Results would sometimes be collected and distributed as random number tables . There are many practical measures of randomness for a binary sequence. These include measures based on frequency, discrete transforms , complexity , or
2380-460: The animals' appearance changing imperceptibly as Turing predicted. In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a painting , drawing , tapestry , ceramic tiling or carpet , but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in
2450-597: The artwork. In mathematics, a tessellation is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps. In architecture, motifs are repeated in various ways to form patterns. Most simply, structures such as windows can be repeated horizontally and vertically (see leading picture). Architects can use and repeat decorative and structural elements such as columns , pediments , and lintels . Repetitions need not be identical; for example, temples in South India have
2520-412: The beginning of a scenario, one might calculate the probability of a certain event. However, as soon as one gains more information about the scenario, one may need to re-calculate the probability accordingly. For example, when being told that a woman has two children, one might be interested in knowing if either of them is a girl, and if yes, the probability that the other child is also a girl. Considering
2590-492: The best deterministic methods. Many scientific fields are concerned with randomness: In the 19th century, scientists used the idea of random motions of molecules in the development of statistical mechanics to explain phenomena in thermodynamics and the properties of gases . According to several standard interpretations of quantum mechanics , microscopic phenomena are objectively random. That is, in an experiment that controls all causally relevant parameters, some aspects of
2660-576: The body plans of animals including molluscs such as the nautilus , and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple . Chaos theory predicts that while the laws of physics are deterministic , there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes. The patterns in nature tend to be static due to dissipation on
2730-497: The children is female, this rules out the boy-boy scenario, leaving only three ways of having the two children: boy-girl, girl-boy, girl-girl. From this, it can be seen only ⅓ of these scenarios would have the other child also be a girl (see Boy or girl paradox for more). In general, by using a probability space, one is less likely to miss out on possible scenarios, or to neglect the importance of new information. This technique can be used to provide insights in other situations such as
2800-427: The context of gambling , but later in connection with physics. Statistics is used to infer an underlying probability distribution of a collection of empirical observations. For the purposes of simulation , it is necessary to have a large supply of random numbers —or means to generate them on demand. Algorithmic information theory studies, among other topics, what constitutes a random sequence . The central idea
2870-415: The die is known to be fair, then previous rolls can give no indication of future events. In nature, events rarely occur with a frequency that is known a priori , so observing outcomes to determine which events are more probable makes sense. However, it is fallacious to apply this logic to systems designed and known to make all outcomes equally likely, such as shuffled cards, dice, and roulette wheels. In
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2940-412: The emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic. Many natural patterns are shaped by this complexity, including vortex streets , other effects of turbulent flow such as meanders in rivers. or nonlinear interaction of the system Waves are disturbances that carry energy as they move. Mechanical waves propagate through
3010-451: The entrance of the court at the beginning of the court day. Originally, the procedure was based on a "first come, first serve" basis. Beginning in 403 BCE, Athenian allotment underwent a series of reforms, and from 370 BCE onwards, they employed the kleroterion. In his Constitution of the Athenians , Aristotle gives an account of the selection of jurors to the dikastra . Each deme divided their dikastes into ten sections, which split
3080-451: The form of a kleroterion . The formalization of odds and chance was perhaps earliest done by the Chinese of 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of calculus had a positive impact on
3150-461: The formal study of randomness. In the 1888 edition of his book The Logic of Chance , John Venn wrote a chapter on The conception of randomness that included his view of the randomness of the digits of pi (π), by using them to construct a random walk in two dimensions. The early part of the 20th century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. In
3220-545: The gods. In most of its mathematical, political, social and religious uses, randomness is used for its innate "fairness" and lack of bias. Politics : Athenian democracy was based on the concept of isonomia (equality of political rights), and used complex allotment machines to ensure that the positions on the ruling committees that ran Athens were fairly allocated. Allotment is now restricted to selecting jurors in Anglo-Saxon legal systems, and in situations where "fairness"
3290-435: The impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal ‘global-forest’ designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal ‘tree-seeds’ which combine to create
3360-677: The influence of genes and the environment), and to some extent randomly. For example, the density of freckles that appear on a person's skin is controlled by genes and exposure to light; whereas the exact location of individual freckles seems random. As far as behavior is concerned, randomness is important if an animal is to behave in a way that is unpredictable to others. For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories. The mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events, originally in
3430-426: The mathematical biologist James D. Murray and other scientists, described a mechanism that spontaneously creates spotted or striped patterns, for example in the skin of mammals or the plumage of birds: a reaction–diffusion system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin. These spatiotemporal patterns slowly drift,
3500-527: The methods used to create them are usually regulated by government Gaming Control Boards . Random drawings are also used to determine lottery winners. In fact, randomness has been used for games of chance throughout history, and to select out individuals for an unwanted task in a fair way (see drawing straws ). Sports : Some sports, including American football , use coin tosses to randomly select starting conditions for games or seed tied teams for postseason play . The National Basketball Association uses
3570-491: The mid-to-late-20th century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness . Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the 20th century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms even outperform
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#17328448020873640-443: The most general empirical patterns of the universe . Daniel Dennett 's notion of real patterns , discussed in his 1991 paper of the same name, provides an ontological framework aiming to discern the reality of patterns beyond mere human interpretation, by examining their predictive utility and the efficiency they provide in compressing information. For example, centre of gravity is a real pattern because it allows us to predict
3710-450: The movements of a bodies such as the earth around the sun, and it compresses all the information about all the particles in the sun and the earth that allows us to make those predictions. Some mathematical rule-patterns can be visualised, and among these are those that explain patterns in nature including the mathematics of symmetry, waves, meanders, and fractals. Fractals are mathematical patterns that are scale invariant. This means that
3780-515: The mutation is not entirely random however as e.g. biologically important regions may be more protected from mutations. Several authors also claim that evolution (and sometimes development) requires a specific form of randomness, namely the introduction of qualitatively new behaviors. Instead of the choice of one possibility among several pre-given ones, this randomness corresponds to the formation of new possibilities. The characteristics of an organism arise to some extent deterministically (e.g., under
3850-998: The other door. Intuitively, one might think the player is choosing between two doors with equal probability, and that the opportunity to choose another door makes no difference. However, an analysis of the probability spaces would reveal that the contestant has received new information, and that changing to the other door would increase their chances of winning. Pattern Any of the senses may directly observe patterns. Conversely, abstract patterns in science , mathematics , or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic , rarely exactly repeating, and often involve fractals . Natural patterns include spirals , meanders , waves , foams , tilings , cracks , and those created by symmetries of rotation and reflection . Patterns have an underlying mathematical structure; indeed, mathematics can be seen as
3920-450: The outcome still vary randomly. For example, if a single unstable atom is placed in a controlled environment, it cannot be predicted how long it will take for the atom to decay—only the probability of decay in a given time. Thus, quantum mechanics does not specify the outcome of individual experiments, but only the probabilities. Hidden variable theories reject the view that nature contains irreducible randomness: such theories posit that in
3990-507: The processes that appear random, properties with a certain statistical distribution are at work behind the scenes, determining the outcome in each case. The modern evolutionary synthesis ascribes the observed diversity of life to random genetic mutations followed by natural selection . The latter retains some random mutations in the gene pool due to the systematically improved chance for survival and reproduction that those mutated genes confer on individuals who possess them. The location of
4060-404: The roll of a die, a coin toss, or most lottery number selection schemes. Truly random processes such as these do not have memory, which makes it impossible for past outcomes to affect future outcomes. In fact, there is no finite number of trials that can guarantee a success. In a random sequence of numbers, a number may be said to be cursed because it has come up less often in the past, and so it
4130-409: The same column. There was a pipe attached to the stone which could then be fed dice that were coloured differently (assumed to be black and white) and could be released individually by a mechanism that has not survived to posterity (but is speculated to be by two nails; one used to block the open end and another to separate the next die to fall from the rest of the dice above it, like an airlock . ) When
4200-407: The same or decrease with complexity. Subsequently, we determine that the local constituent fractal (‘tree-seed’) patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference
4270-483: The search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world. In many areas of the decorative arts , from ceramics and textiles to wallpaper , "pattern" is used for an ornamental design that is manufactured, perhaps for many different shapes of object. In art and architecture, decorations or visual motifs may be combined and repeated to form patterns designed to have
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#17328448020874340-497: The sense that the expected value of their change is zero but the actual value may turn out to be positive or negative. More generally, asset prices are influenced by a variety of unpredictable events in the general economic environment. Random selection can be an official method to resolve tied elections in some jurisdictions. Its use in politics originates long ago. Many offices in ancient Athens were chosen by lot instead of modern voting. Randomness can be seen as conflicting with
4410-519: The shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their formation can be simple (e.g. Lindenmayer systems describing tree shapes). In pattern theory , devised by Ulf Grenander , mathematicians attempt to describe
4480-425: The skeletons of silicoflagellates and sea urchins . Cracks form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics. Alan Turing , and later
4550-426: The two events independently, one might expect that the probability that the other child is female is ½ (50%), but by building a probability space illustrating all possible outcomes, one would notice that the probability is actually only ⅓ (33%). To be sure, the probability space does illustrate four ways of having these two children: boy-boy, girl-boy, boy-girl, and girl-girl. But once it is known that at least one of
4620-459: The use of two kleroteria . Candidate citizens placed their identification token ( pinaka ) in the section's chest. Once each citizen who wished to become judge for the day placed their pinaka in the chest, the presiding archon shook the chest and drew out tokens. The citizen whose token was first drawn became the token inserter ( empektes ). The token inserter then pulled out tokens and inserted them into their corresponding sections. The kleroterion
4690-485: The various applications of randomness . Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods , which rely on random input (such as from random number generators or pseudorandom number generators ), are important techniques in science, particularly in the field of computational science . By analogy, quasi-Monte Carlo methods use quasi-random number generators . Random selection, when narrowly associated with
4760-729: The world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner. In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns. A recent study from Aesthetics and Psychological Effects of Fractal Based Design suggested that fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on
4830-474: Was a randomization device used by the Athenian polis during the period of democracy to select citizens to the boule , to most state offices, to the nomothetai , and to court juries. The kleroterion was a slab of stone incised with rows of slots and with an attached tube. Citizens' tokens— pinakia —were placed randomly in the slots so that every member of each of the tribes of Athens had their tokens placed in
4900-405: Was divided into five columns, one column per tribe section (between two machines). Each row was known as a kanomides . Once the token inserter filled the kleroterion, the archon then placed a mix of black and white dice ( kyboi ) into the side of the kleroterion. The number of white dice was proportional to the number of jurors needed. The archon allowed the dice to fall through a tube on the side of
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