@normonics' Intro to Applied Complexity #ACS101 #SpringA2021 Highlights
Session 4: Cellular Automata, Self-Organisation, and Pattern Formation
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Session 4: Cellular Automata, Self-Organisation, and Pattern Formation
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https://twitter.com/evolvingcalm/status/1365752684662296576
How do we get Order without a creator?
Self-organisation
1/n
Self-organisation
1/n
DNA is not a blueprint, a common but bad metaphor.
DNA serves as a set of internal instructions to tell a cell what do I do given these inputs from my local environment.
2/n
DNA serves as a set of internal instructions to tell a cell what do I do given these inputs from my local environment.
2/n
As if a pile bricks interacting together formed a house spontaneously.
3/n
3/n
Distributed agents engage in 'local' interactions and behaviours, order forms 'globally'.
4/n
4/n
Consider the example of the micelle
(Also think about attractor dynamics)
5/n
(Also think about attractor dynamics)
5/n
One way to think about a pattern is if something is compressible then there is a pattern.
A pattern is some kind of redundancy of information.
Mutual information is shared by components/elements by virtue of them being part of a pattern.
6/n
A pattern is some kind of redundancy of information.
Mutual information is shared by components/elements by virtue of them being part of a pattern.
6/n
If something converges it can almost be treated as one dimensional.
But higher dimensional representations are more faithful.
7/n
But higher dimensional representations are more faithful.
7/n
"We have no choice but to develop a whole new kind of intuition" - Stephen Wolfram 'A New Kind of Science'
8/n
8/n
Think about what is the possibility space of all alternatives.
You can try them and see what they do.
9/n
You can try them and see what they do.
9/n
Again it's hard to be random intentionally but you can try.
10/n
10/n
Emergent behaviour is not baked in any explicit way into the rules.
The rules are the rules, then these behaviours and patterns emerge out of the rules without ever being explicitly coded anywhere, only implicitly.
11/n
The rules are the rules, then these behaviours and patterns emerge out of the rules without ever being explicitly coded anywhere, only implicitly.
11/n
Coarsening is where the smallest details become larger, and the finest resolution of the pattern goes up as the system evolves over time.
12/n
12/n
Out of elementary cellular automata you can get something as rich and powerful as all our computers as Rule 110 demonstrates.
A potent lesson.
13/n
A potent lesson.
13/n
In the real world interface always matters.
15/n
15/n
Is your interface right for a human being?
16/n
16/n
The panic rule is a highly simplified system.
But the idea of contagion as human behaviours is very real.
(Clearly something we have to grapple with)
(0.25% or 0.03%?)
appliedcomplexity.io/ca_panic/
17/n
But the idea of contagion as human behaviours is very real.
(Clearly something we have to grapple with)
(0.25% or 0.03%?)
appliedcomplexity.io/ca_panic/
17/n
A small parameter change can cause a massive regime change.
18/n
18/n
A phase transition can always sneak up on you.
19/n
19/n
Trying to look at a system empirically doing statistics you can miss a jump easily.
People apply linear regression and get it completely wrong all the time.
20/n
People apply linear regression and get it completely wrong all the time.
20/n
They don't know what they don't know.
21/n
21/n
To form a pattern for things to not disintegrate into maximum entropy/disorder you need your system to be open to flows of energy and matter.
Isolated systems disintegrate.
22/n
Isolated systems disintegrate.
22/n
We see pattern forming a lot in biology but it actually doesn't depend on biology explicitly. It only depends on being an open system where order can form.
(referred to as far from equilibrium systems, as opposed to equilibrium systems/isolated)
23/n
(referred to as far from equilibrium systems, as opposed to equilibrium systems/isolated)
23/n
Think of physical systems like sand & water or stripes on an animal.
24/n
24/n
Both are examples of 'Long-range inhibition, local activation' - another bottom-up pattern where each unit/cell/agent follow a rule to do the same as its nearest neighbours & the opposite of its distant neighbours
(also a universality class).
appliedcomplexity.io/ca_lali/
25/n
(also a universality class).
appliedcomplexity.io/ca_lali/
25/n
'Long-range inhibition, local activation patterns' form and stabilise as self-contained wholes.
26/n
26/n
A universality class is when two or more natural systems map to a formalism.
28/n
28/n
When we build things mathematically/computationally we have formal systems.
When we look at things in the world we have natural systems. They are not formalised in any explicit way.
29/n
When we look at things in the world we have natural systems. They are not formalised in any explicit way.
29/n
Often in science we are trying to relate the two - formal to natural.
Natural systems have causality.
Formal systems have inference (we treat inference in formal systems as causality).
30/n
Natural systems have causality.
Formal systems have inference (we treat inference in formal systems as causality).
30/n
It's remarkable how much genuine mystery there still is in the details of something like a snowflake.
Snowflakes turn out to be a complicated story.
31/n
Snowflakes turn out to be a complicated story.
31/n
Symmetry breaking is a pervasive idea that can show up in a variety of ways as a consequence of small perturbations.
32/n
32/n
The patterns like 'long-range inhibition, local activation' have a characteristic scale.
This complements patterns without a characteristic scale like fractals.
33/n
This complements patterns without a characteristic scale like fractals.
33/n
Complex systems have some kind of balance and interplay of both positive and negative feedback interactions.
34/n
34/n
In a phase transition it's not necessarily the case we can come right back.
This is called Hysteresis.
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This is called Hysteresis.
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