Two species of cellular automata: one which is big (2x2) and one which is (1x1)
Both move in a random walk
They move one step each time, and leave holes behind. Holes have a fixed probability to be filled
Big ones kill the small ones when they move in, and have a fixed death rate
Speciaes replicated when they have move from a hole to the soil, as resources are on the boundary.
Rate for death (when moves into a vacant space), rate for birth (when you move into birth), rate for hole filling
Calculate the density and fraction of soil-vacant walls.
Tuesday afternoon: Group meetings
Wednesday 10:30: Guest Lectures
Do a plot of characteristics over time to look for oscillation.
Do it with random connections, and then you can use a mean-field comparison. Compare DEs to the solution.
Logscale x and y
Asymmetry: bacteria ned to live longer than the holes
Check newrepro rate and reset simulation
Every time step: move all bacteria: Set a number of bacteria to move every time step, each can move multiple times. One movement per bacteria
Calculate cluster size distribution.
Do log-log axes on heatmap viz
Try to make everything stochastic: choose a point, and depending on what it is, do something (fill/die/move)
If it’s a bacteria, check for death, and if not make it move
Do phase space diagram for mean field model
Analyze meanfield soln by looking at bifurcation
The area where bacteria dies in mean-field and survives in neighbours could be relevant?
Do for 50x50, less phase points
Try to do it with lower birth rate
Make visualizations for every state, put them next to each other
Visualize the nullcline: B-E landscape, change the parameters and see wher the fixed point
Try mean field
Try to quantify some sort of spatial structure which is causing the difference between mean field
Potentially try 3d.
Pick a random side, you’re going in an ordedred way.
Make hybrid model, where you reprouce anywhere.
Find out how to vsualize 3d
Top triangle possible due to the sparsity of empty spaces.
Try to measure the spatial corrrelatials: the soil autocorrection.
Do emanfield for r=0.1
One animal eats it’s own environment, and thus it dies out faster than mean field?
CML: if density is coming in, reduce it by prob 1/d
Don’t conserve d
Different types of vacancies, red bug can give the blue bug.
If red moves into blue, make it swapping
Slow repro rate, at a rate that would kill meanfield but locality stays alive
Try jumping far as well, and if you jump far, you have a chance to die
Meanfield scaling r and d the same way doesn’t change results
Try to do it with a larger lattice size and see if it approaches meanfield
Correct bug with red living and blue dying
Try nutrient, soil, empty, bacteria. Bacteria leave behind nutrients, and only replicate in them
If you move into soil, chance to replicate + chance to die
Try doing the soil filling only if your neighbours are soil
Do mean field corresponding to soil neighbour
Check inside boundary of soil neighbour, is it still critical
Reduce replication rate and try
Add nullclines to presentation
Consider exploring nutrient model (to have bacteria support each other) and coupled map lattice
Do a bigger simulation and see if cutoff changes
See if exponent is independent of parameters s,d
Try to quantify scaling r,d
Search for predator prey model on lattice
Check power law in predator-prey
Do the meanfield for the predator prey
When moving in, take over, or try to annhiliate
Low death rate: soil is limiting, high death rate: empty space is limiting. Empty space is collapsing: bacteria deaths give empty sace, but not enough to compensate for empty space created in bacterial movement. No empty space causes bacteria to die out, which gives the phase transition.
Try to write the equations for the nullclines in both cases.
Try to do the 2 species with difference in death rate
Measure the boundary of cluster sizes. Fractical dimension of boundary
CML: measure autocorrelation without defining clusters
Think about using gradient instead of linear in CML, to emphasize boundaries
Two species meanfield, and check fractions of red/blue
Gather more data for single species power law
Lotka voltairre with competitive exclusion
Microscopic biofilms(?)
Presentation notes:
Show predator prey vs meanfield
Add axes labels
Add a little discussion on power law
Remove the bad model
Remove the top heatmap
Explain predator-prey better
Check if oscillations disappear with system size
calculate worm-worm correlation
Correlation function in space
Try reducing parameters by a facter and see if it changes stuff
Start from different survival rates:
Normalize the correlations
Try CML with new dynamics
Check cluster size dist for nutrient
Try changing the death rate and look for changes in the exponential for the worm-worm correlation
Check if changing the birth rate changes the worm-correlation
Check cluster size dist for different positions where it dies in meanfield
maybe check bistability in lattice model
Try adding nutrient to CML
So 200x200 and see if power law changes
Check fixed soil filling rate, vary death rate
Try to replicate paper with 2-d
Try to make worms die from starvation: they die in white and live in soil
Check in what region the power law is seen
Check if power law changes with soil filling rate
Worm -> Worm: kill the other worm
Small difference in the soil methodology
Try to calculate CSD for weird fractal dimension plot
At what point does the cutoff enter in 2d
Look for powerlaw regime with largest cluster size (1 order of magnitude less than system size)
Do the 3D raster
Try largest linear dimensions: both cumulative and in fractal dim
Normalize by the amount of soil in the system: cluster as % of total soil
CONNECT NUTRIENT AND WORM for clusters
lattice in worm oscillation amplitude (ratio in logscale)
Choose a soil site, and find the cluster size containing it over time. Move cluster along
Calculate effective soil filling rate
Show 3D over time (CSD)
Make 2D oscillations
Try smaller regions and see if the oscillations are visible
Max divided by min (or mean), to see the sensititity. Want to see how close it gets to “dying out”
Try the two species model
Try to keep a limit at 10^-6 in the meanfield
Try seeing if it comes back
2D, look at time series of the entire system, half system, quarter system, etc
Increase soil filling rate: multiple tries?
Try two species
Time distribution between soil disappearing and soil reappearing at a point
Look for oscillation in region where it survives in lattice but dies in mean-field
Check time period correlation between lattice and mean-field
Check how soil filling rate and death rate affect the exp decay rate
Check other lifetimes such as worm
Check meanfield death due to worm/empty/soil (in both regions, left and down, what’s the cause?)
Check if oscillatory counts in 2spec
Check counts of simulations (see if coherent-oscillatory)
Try two spec with the same nutrient needed for both (maybe adding nutrient increases death rate)
Plot oscillation amplitude vs system size
Never let worm go below 10^-6
Check oscillations in 2d
Do well-mixed
Look up spiral simulation
Try extreme case, 1 parasite, and 1 good worm
Look up other examples where oscillations => survival in lattice
Play around with tradeoff on death rate / nutrient production
Consider a distribution in parameters or allow parameters to mutate
Try parasite model in 2D
Population dynamics with delay DE : chaos
Check oscillation in yellow region
Check structure in yellow region
Can sustain multiple parasiets?
In parasite model, check lifetimes.
Run Lotka volterra for nutrient without nutrient to see difference for IUPAB
Play around with mu tradeoff being theta instead of rho
Check if power law at the top left point for CSD
Do more exhaustive check for oscillatory parasite, by checking lifetimes
Work on IUPAB abstract
Check 2D front or oscillations for large systems: maybe with rigid boundaries?
Lotka-Volterra: soil_neighbour_rasterscan.html, try to look for oscillations
Make the blocks smaller
Let blue swap places with soil, and see if oscillations retrun
Check correlation of diversity with power law
Read more about soil composition: empty fraction, living fraction, inorganic fraction
Try to generate a ton of differently-sized particles, from a power law dist of varying exp, and drop them and see the packing fraction
Try to do multiple worms in hogweg paper
Try to put a 3rd species in to eat the parasite
Check soil lifetimes calc
Check that blue dying doesn’t give oscillations
Change mu1 to 1
Check if reducing deathrate of blue gives oscillations
Try to see if you can get a big clump + poweralw in nature
Look into dust powerlaw some more
Not much to discuss, showed Kuni the Hogweg plots
See if there’s a long-term segregation in 2D hogweg
Dragon king state, chimera state (with decoherence)
Try 3D lattice visualization
Try different number of species
Try removing soil
Try moving into soil and replicating, and see if that changes localization
Try getting better params for localization
Check localization characteristic size
Check 2 clumps evolutions
Check cluster size of non-soil
Check if inside the cluster, you have soil as a power law
Try to do with parasite model localization
Try nutrient fast and worm slow
(No kim, so spontaeneous meetings with Kuni)
Check for parasite localization
Check for powerlaw during parasite localization
Check whether LargeCluster + power law occurs more for parasite than single species
Potentially look at CML coarse-graining, with a spatial correlation for soil PSD?
How does the parasite affect the rasterscan: 2D with parasites, for rel rho = 4 and 2
Check if coexistance is correlated to powerlaw (check powerlaw for various regions inside the rasterscan)
Try to see if mutation can remove a parameter (relative birthrates)
Check whether the critical points are different
Calculate mass vs largest linear dimension of clusters
Look at clusters for different
Are we really the first to do this?
Start with one point and see if it grows, in our model
Check for percolation cluster size dist exponents (are they 1.8?)
Maybe, when looking each direction, you might have 2 directed percolation critical points. Unless one is site and one is directed, in which case you can have 2 different critical points
Critical region may be smaller, but it may still exist in dirP
Kim’s Percolation: every site, if at least one neighbour, it’ll be alive
Check whether z exponent is just from left to right distance, and try to calculate that (it’s probably the same as R^2)
Check if powerlaw is valid for different values of sigma, and if grassbergers exponents are as well
Dimension 1: drawing boxes, plot N(boxes) vs box size Dimension 2: plot mass of each cluster vs largest linear dimension of that cluster Dimension 3: Reduce every cluster to a point (within the cluster), and do box counting on the points
Also check if after fixing bug, correlation between survival and power law
Check information dimension, which doesn’t agree with box. $P^2$
Check also correlation dimension. Also Grassberger dimension $P^1$
Check for DP for empty sites
Look at parasite reproduction rate correlation with power law
Bethe lattice exact renormalization can be done, so this can be seen.
Try bethe lattice! Ignore ESPL, and look for FSPL correlation with DP point