5.3 Emergence Flashcards
State the three ways that complexity can arise at the microscopic level
- Competition
- Symmetry breaking
- Threshold dynamics
Describe competition in terms of complexity, and give examples
It is being like neighbour vs doing their own thing
e.g. ferromagnet, flocking, synchronisation
Describe symmetry breaking in terms of complexity, and give examples
e.g. termites, preferential attachment, segregation
Describe thereshold dynamics in terms of complexity, and give examples
Separation of timescales from self similar bursty dynamics
e.g. Avalanching, self organising critically
Briefly describe the symmetry breaking termite model
Termites wander randomly, non-interactinfg
- Carry one piece of wood
- If they come across wood, they drop current one, then pick it up
Briefly describe the symmetry breaking segregation model
2 Populations which start at random positions
- Individual agents move until they achieve % similar neighbours
- Get a tendency to segregate
Briefly describe the symmetry breaking preferential attachement model
Add nodes one at a time
- Probability of connection to an existing node is proportional to the current number of connections
- Get a power law and an exp. decay type histogram
Briefly describe the symmetry breaking diffusion limited aggregation model
Particles fall vertically and stick on another particle
- New particles can only land on existing ones
- Get plant/tree growth vertically
Briefly describe the thresholded dynamics avalanche model
Add rice grains slowly and redistribute if local gradient exceeds a critical value
- Avalanches are faster than feeding rate
- Avalanches on all sizes and a power law
- System moves through metastable staes rather than towards equilibrium
Describe the self similar tree
Rule: Each branch grows 3 more branches, 1/5 as long as itself
N = 3^a, L = 1 / (5^a)
- Get a exp. type decay histogram, and can only measure over a finite range of L
