A Pattern is a schema.
According to General Schemas Theory a Schema is a projected organization of spacetime as an a priroi synthesis that we intuit (speaking in Kantian terms) which serves as a template of understanding.
If you start with Systems Theory and ask what is the next threshold of abstraction up which includes Systems Theory but other similar but different theories, then you get General Schemas Theory. It is just like General Systems Theory but the next level of abstraction up. So at that level we can name several schemas that definitely exist within Science such as monad, pattern, form, system, etc.
It is interesting that no discipline of General Schemas Theory has been posited up til now that I can find. I especially expected to find it in Art Criticism or Architectural Criticism, but have not found it defined elsewhere beyond my own work.
The best work on Schemas in general within our tradition is Umberto Eco’s Kant and the Platypus.
In this book he defines Mathematical and Geometric Schemas and that is what I mean by the term “Schema” with respect to General Schemas Theory.
Grenander is the only mathematician I know of who has created a mathematics of Pattern. http://www.dam.brown.edu/pattern/ug.html
I order to get General Schemas Theory off the ground as a discipline I devised a speculative hypothesis called Sprime. In Sprime we posit that there are ten schemas and that they form a nested hierarchy of scopes at different dimensional scales. Sprime also posits that there are two schemas per dimension and two dimensions per schema. Schemas start at the negative first dimension and go up to the ninth dimension. Thus the series of schemas from the point of view of the Sprime hypothesis is as follows:
F Theory 12
M Theory 11
String Theory 10
Pluriverse 8, 9
Kosmos 7, 8
World 6, 7
Domain 5, 6
OpenScape (aka meta-system) 4, 5
System 3, 4
Form 2, 3
Pattern 1, 2 <<<<<<<<<<<<<<<<<<<<<<< as defined by Grenander
Monad 0, 1
Facet -1, 0
Unknown -2, -1
Now there are some interesting things about the nested hierarchy of organizations of different scope an scale. One is that Monads can either be dimensionless points or one dimensional strings, thus string theory is really a variation on monadology. Next Pattern has two dimensions in which it exists which is as a string with some contents that can form a pattern, like 1 and 0 of memory. But the most interesting patterns are two dimensional, for instance the patterns which form in the Game of Life, or are created in Fabrics, etc.
Notice also that we can consider the nesting in either direction, so we can consider that patterns form the content of forms either two or three dimensional, but also we can consider that there are Patterns of Forms, or Patterns of Systems etc. Patterns of Forms are the most prevalent and we call that after Alexander Pattern Languages which we now apply to Software design as a way of leveraging knowledge within the Software Engineering discipline. So Patterns are not trapped in their dimensions but instead can modify other schemas either of greater or lesser scope.
Schemas are of limited scope and of finite number. So they only go up to the 9th dimension. It is interesting that we do not seem to have schemas at the tenth dimension and higher where string theory plays out, and so string theory is difficult to understand, because we do not have any templates by which to understand it already available. The basic insight of Schemas theory is that spacetime as we project it as an a priori synthesis that is intuited according to Kant is striated and not unstriated, i.e. not a homogeneous plenum. In fact in Bernstein’s lectures on Critique of Pure reason that I read recently he criticizes Kant on this very point of not having different layered concepts of time but only one, and I think Schemas Theory points us to the fact that space also should be considered as striated, i.e. there are different ontological templates of understanding that are projected on it at different scopes and scales.
The other interesting thing is that our tradition was dominated by the Form Schema from its inception up until the beginning of the last century, at which time both System and Structure (pattern) became more overtly significant Schemas. Now we are becoming more interested in Patterns and Domains.
I have written about the Pattern Schema as part of the research for my dissertation at http://about.me/emergentdesign.