Patterns are relationships of a particular sort: a relationship between one entity and a set of others, where the first is judged to represent and simplify the others.
The American philosopher Charles Peirce has placed the “universe as a web of patternment relationships” perspective in a broader context by introducing the basic philosophical categories called First, Second and Third.
First = pure, unprocessed Being
Second = reaction ... the raw feeling of one thing having impact on another
Third = relationship (the raw material for pattern: patternment is a particular, critical kind of relationship)
One can also push further than Peirce did, following other thinkers like Jung and Buckminster Fuller, and posit categories like:
Fourth = synergy ... networks of relationships spawning new relationships
In this perspective the view of Cosmos as pattern-space is the perspective of Thirdness.

Isn’t This Just a Bunch of Abstract Nonsense?
This sort of abstract categorization of Cosmos doesn’t do much in itself ... but it provides a general perspective that can be useful for addressing concrete issues.
We will use this categorial perspective to approach the topics of awareness and consciousness ... which are critical to various issues that will confront us as technology develops, such as immortality, AI and uploading.
Philosophy pursued in the absence of practical issues tends to become verbal or intellectual gamesmanship.
Practical issues pursued in the absence of appropriate philosophy tend to lead to various sorts of confusion—which can be fine, but given the sensitivity of the point in human history we’re approaching, serious attempts at confusion-minimization seem indicated!
This brief article is part of the overall Cosmist Manifesto.
Numerology aside, Peirce was on to something. Indeed there are three core ontological primatives or categories, but I think they are somewhat different to what Peirce thought- his are too vague and poorly developed. Here are my 3 modern ones:
Identity: Internal properties of things - properties which define the structure or raw materials comprising a stable object.
Function: Functional properties - similar to Use Cases in UML, externally observable effects.
Interface: Representational properties - properties interpreted as signals and symbols
Basically, everything in a given domain can be initially classified as either Identity, Function or Interface (your ‘synergy’ is not a fourth category, it falls under Interface).