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# What is a Spatio-Temporal Pattern?

In our everyday language the term pattern is often used as a synonym to regularity. We use pattern in combination with time, sound, space and also to describe the structures behind our thinking 2.1. There are two opposites of the term pattern. If we are not able to recognize any pattern, we may state that there is no pattern. The second way often used in the case of spatial data to describe the absence of a pattern is regarded as a separate class of pattern, the random pattern. Hudson and Fowler (1966) define pattern as '.. the zero-dimensional characteristic of a set of points which describes the location of these points in terms of the relative distances of one point to another'. This definition has strong resemblance to the hypothesis no. 3 in the introduction, that in this case space and spatial arrangements can be described by a single value.

We often use the term spatial pattern. What is meant by that expression? In the case of point objects this question is mostly reduced to the aspect of whether the objects are arranged randomly, clustered or evenly distributed. In the latter two cases inferences about the underlying mechanism are drawn from the data themselves as whether the distribution of the objects may be formed by a Poisson-, Cox-, Markov- or a similar kind of process. In the case of linear elements the literature is astonishingly quiet about statements of patterns in spite of their wide use as a representational form in Geographical Information Science. Common examples include elements such as streams, roads or border lines of certain habitat descriptives. In the case of polygonal data models a variety of aspects can be considered for analyzing pattern. Juxtaposition, interdispersion and measurements of size and shape are a few examples for describing certain aspects of arrangements and their regularity in polygon structures. Fields as another type of data model have their own set of descriptives for characterizing inherent patterns (e.g. variograms, Fourier series etc.). The idea of patterns with this kind of data is often viewed as regularities as surface trends or periodical wave forms.

Most definitions of pattern state that pattern should be defined independently of scale. Aside from the fact that this is very difficult to achieve, it also contrasts the common use often found in the biological literature. As an example an animal using one hectare as its homerange is considered to show a different pattern from another one using 100 hectares just because of the areal difference. The distribution patterns often used in faunistics are another example where the requirement of scale independence is ignored. In linguistics it may be argued that these are two different terms hiding behind the same word. For scientific information transfer this is an awkward situation.

The terms pattern and different pattern are often applied in situations where a more concrete definition would sound cumbersome. As there are many aspects being considered in the process of analysis, the term pattern is often hiding a concrete finding. Using the expression '... it shows a different pattern' often pretends to have found a more general or globalised difference where in fact only one aspect was analyzed.

Because of the above reasoning I think the use of the term pattern should be limited to descriptions of theoretical ideas, and in the case of concrete study results more appropriate and concrete descriptions of the actual findings should be used.

Temporal patterns are probably best explained using the global language of music. On an abstract level it can be defined as a consecutive, organized arrangement of sounds. The melody consisting of tone level and rhythm can be considered as pattern homologous to the case of spatial phenomena. The speed at which a melody is played does not change the pattern. Interestingly the gamut used in singing a song does not alter its pattern, neither. Maybe we can find some causes of confusion in this context. Gamut and scale in the case of music can be used as synonyms. Transcribing a melody from C-major to F-major does not change the melody, but 'scaling' the tones by a factor for example 1.5 by altering the tone frequency from 400 Hz to 600 Hz, 460 Hz to 690 Hz and so on, will change the melody or even make it unrecognizable.

As it was illustrated above, there exists a variety of definitions, aspects and applications of the term pattern. In this thesis I will use the following definition: Pattern is a general term for any recognizable regularity in the data.

After looking at spatial and temporal aspects of patterns, we need to examine the often encountered term spatio-temporal pattern. As the term implies it describes a phenomenon which requires both spatial and temporal regularities to occur. A simple change in the spatial arrangement does not fulfill the requirement for a spatio-temporal pattern. A simple change in speed does not fulfill the requirements, neither. It is the combination of both space and time which needs to express regularities. Alterations in space which do not contain temporal regularities may be best named spatial change. If the regularities are changing, it may be expressed as a change in the specific spatial pattern.

An example for a spatio-temporal pattern can be found in car accidents with animals. They occur at different rates during the daytime, week and season and express 'preferences' for certain locations. Accidents with animals as red or roe deer for example mostly happen during dawn and dusk time. They vary according to the altitude of the sun changing during the year. These kinds of accidents occur more frequently during seasons where migrations take place. But then they often happen at locations different from the ones normally encountered during the year. In this case we have clear spatial and temporal regularities which in combination form a good example for a spatio-temporal pattern.

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