There are already lots of ‘system’s or ‘networks’ within audio-visual compositions… TouchDesigner itself is the most representative node-based audio/visual system-network. But these are abstractive audio-visual based and come with limitations when talking about semantics/other visual interfaces rather than abstractive a/v.

When constructing multi-layered system art, there can be lots of approaches - but one of the possible approaches is to reference existing ‘systems’. (This might act as a good starting point rather than 맨땅에 헤딩) 
There are already lots of ‘visual states’ in existing ‘audio/visual systems - compositions’ - Some real-time, some interactive - especially within touchdesigner, but also appeared in kinetic art. For touchdesigner, they are literally node-based system where input and network combination creates an audio-visual output - a composition of states - and therefore no matter how the output a/v appears to be complex - it is composed of states, and if the input variable changes, than the output changes accordingly. Similar to kinetic art - usually employs a combination of unit modules (lights are the most conventional) and its ‘states’ turn on, off, intensity, etc… And this modular combination creates a whole system. Which is again, composed as a combination of states.

In interactive/computational art, it is important to analyse these states and compose complex systems based on the repetition and modularisation of these states. I think this rule for composing audio-visual networks can be also similarly used for systematic/semantic arts - It’s just the domain that it’s different, but the foundation remains the same.

Also association btw system-semantic state and visual state is quite important as you will need to eventually express/plot the systematic state into visual/audio-visual format. Understanding and composing this interconnection carefully is crucial.

For example, there are lots of employment of boolean states in traditional visual states - Kinetic light on-off most representatively. Also in the systematic state - imagine multiple grids with each being a module. Modules might be turned on <-> off repetitively to create an overall visual composition. Or switching between different states: ≠ employs this technique quite effectively. (≠ had a bit more complex inner states though)  B <-> W bg composition is also one of the most representative way of plotting. Semantically, there are lots of situation where we need to use boolean/turn on <-> off/binary systems to depict the module’s inner-state, so this strategy might be effective.

These discrete states (0/1) can be expanded to (0-n) discrete states: State A, B, C. For Example: A single unit of the semantic system might have three different states. This might correspond to the selection of R, G, B channels, for example when visualising. If there are 4 states - visually use N/S/W/E.

What about continuous states/continuous variables? Visual State: Intensity. System state: Lots of occasions when you have to plot conti’ numerical value, like monetary value ($), representatively. Also important to plot this conti systematic value visually - use a different intensity of colours, space, angle, etc. Data sonification is also a useful answer. Also you can use a threshold to make the conti variable into boolean – If the (V > Threshold) (true/false).

The most representative example – Space Odyssey scene when HAL is killing sleeping pilots - how the texts turns into ‘system malfunction’ and the graph responds to this change - is a good way of how visual state and system state combined.

Here we talked about relatively simple states, individual module-based states. However, a more complex system is possible once we find out the clear association between visual state and system state - recall how touchdesigner have so much of a complicated visual system and network - the semantic system should follow the same trace.

For this association/expansion towards the complicated system to be possible, as of TouchDesigner’s network, we need to build a similar system - a sort of a network for the system art - which I will reference more to the Graph Theory G(V, E) structure. V → State/Node, E → Edge/relationship.

V → Input nodes, Systematically pre-set nodes, context nodes, etc.
E → Relationship btw nodes, defining the relationship

Note that this is very high-level conceptual approach, not really going to the node-based structure itself…

That does not mean that the system art should necessarily have a node-based structure - I think the foundation might stick the same, but its graphical structure should be different from the TouchDesigner’s node-based structure/node-based UI. Because these system art’s graph art is a CONCEPTUAL one. Still need to further define the relationship between the mathematical graphs and system art…

Let’s also talk about the conversion of ‘ingredients’ – Audio/visual art has literally audio and visual elements as their ingredients. For System state it can be extend to

Texts (Lots of people doing this already)
Numbers (As of the case of Present Shock - UVA)
Generative Images/Videos (Also easy to think of - lots of people doing this)
Graphs (Bar/Chart/Dashboard/Combined)
Websites 
Commercial UIs - Advertisement, Business Card, Flight Information, Chatting UIs
Maps (Multiple Maps or Single Map and multiple modalities)
Avatar/Profile/Agent
Complex Networks
3D Structure (Modular - just like SoTA)

And any other thing that can be possible composed/widely communicated within web frameworks..

And these ingredients can have states - just as visual elements have states. This might offer a good starting point.

THOUGHT-EXPERIMENT: ONE EXAMPLE

Abstractive/Conceptual Example about the time (linearity of time)
Aesthetic: Grid Layout, All modules first initially a digital clock HH:MM
HH:MM

INITIALLY: HH:MM synced with real time
AS PEOPLE INTERACTS: (IDK WHAT exactly the interaction will be) but the gradient/speed of time starts to differ based on the coordinate of the time module (x, y)
→ This different speed indicates the non-linearity of time and distortion in a spatial-temporal dimension, tilted based on the interaction
AS INTERACTION INTENSIFIES: The digital time display HH:MM starts to change (differs from module) into 1) analogue clock, 2) different design of digital clocks, 3) generative images/audios, 4) graphs, 5) clocks presented in different visual design elements (reference to christian marclay), etc…. And this is presented chaotically… based on the different speed/role that each timer module is playing
AS INTERACTION END/USER LEAVES: Each time module gradually moves back to the original setting (digital clock HH:MM synced with real time)
IF MULTIPLE USER PLAYS IN SAME TIME: It amplifies the interaction. This example is based on a state-based approach rather than traditional linear/progressive storytelling. (Multiple) Interactions can be amplified/disamplified - interfered - just as how two or more waves interfere. It is up to multiple users interacting simultaneously on how they will control this: A WAVE INTERFERENCE. AN INTERACTION INTERFERENCE

Time-Object axis: Converting the time in x-axis into time in y-axis (matter of gradient of time)

Note that specific narrative for this artwork is TBD

Significance of this system: It connects visual state - system state successfully.
It also approaches from system-based approach (i.e. no single user, no linear narrative, no  clear start or end, just an equilibrium and off-equilibrium dynamic state) 
Each system state is closely connected with the visual state - digital clock, analogue clock, presentation of different clocks… Is significant
Also it closely & intuitively talks about the concept of time in an abstractive/interactive language