An Analysis of Jenga Using Complex Systems Theory. Avalanches. Wooden Blocks. Spherical Cows. By John Bartholomew, Wonmin Song, Michael Stefszky and Sean Hodgman. Jenga – A Brief History. Complex Systems Assignment 1:. Developed in 1970’s by Leslie Scott
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An Analysis of Jenga Using Complex Systems Theory
Avalanches
Wooden Blocks
Spherical Cows
By John Bartholomew, Wonmin Song, Michael Stefszky and Sean Hodgman
Jenga – A Brief History
Complex Systems Assignment 1:
Jenga - The Game
Complex Systems Assignment 1:
Jenga - A Complex System?
Complex Systems Assignment 1:
Jenga - A Complex System?
Complex Systems Assignment 1:
Motivation?
Complex Systems Assignment 1:
Ultimate Jenga Strategy
Motivation
Complex Systems Assignment 1:
http://landslides.usgs.gov/images/home/LaConchia05.jpg
http://www.ffme.fr/ski-alpinisme/nivologie/photaval/aval10.jpg
Power Law
Frette et al. (1996)
Turcotte (1999)
Self Organizing Criticality
Frette et al. (1996)
Complex Systems Assignment 1:
Sandpile model
Complex Systems Assignment 1:
Minor perturbation can lead to local instability or global collapse – ‘avalanche’
Avalanche size:
2
Sandpile model
Complex Systems Assignment 1:
Cautious way forward…
Complex Systems Assignment 1:
What We Did
Complex Systems Assignment 1:
From This
To This
Strategies
JENGA
JENGA
JENGA
JENGA
JENGA
JENGA
JENGA
JENGA
JENGA
JENGA
JENGA
Complex Systems Assignment 1:
Middles Out
ZigZag
Side 1
Side 2
Middle Then Sides
Side 1
AND FINALLY…
An optimal game strategy where we would start from the bottom and work our way up, pulling out any bricks which were loose enough to pull out easily
Side 1
Side 2
All Outside Bricks
Side 1
Side 2
Many Strategies So We Could …
Complex Systems Assignment 1:
Whoooooaaaaaaa!!!!!!!!
What We Expected
Complex Systems Assignment 1:
Results – Stability Regions
Complex Systems Assignment 1:
Complex Systems Assignment 1:
Complex Systems Assignment 1:
Results – Different Strategies
Complex Systems Assignment 1:
Results
Complex Systems Assignment 1:
Not Enough Data to definitively rule out one distribution, Gaussian and Cauchy-Lorentz look to fit data quite well
Results – Step Size Blocks Removed
Complex Systems Assignment 1:
Results – Step Size Blocks Remaining
Complex Systems Assignment 1:
Results – Step Size Maximum Distance
Complex Systems Assignment 1:
Results – Memory effects?
Complex Systems Assignment 1:
Modeling – Another Spherical Cow?
Complex Systems Assignment 1:
Universality of network theory:
Topology of networks explains various kinds of networks.
Social networks, biological networks, WWW
Why not Jenga?
Look at Jenga layers as nodes of a network with: specified fitness values assigned to each layer, and each layer is connected to the layers above it.
This simplifies the picture for us to look at 18 layers, not at all 54 pieces!!
Modified sandpile model
Complex Systems Assignment 1:
-As mentioned before, the sandpile model eliminates least fit cells of sand Selection law: life is tough for weak and poor!
-The whole system self-organizes itself to punctuated equilibriums due to the memory effect.
- Our case is a bit different.
Fitness & The Magic Number
Complex Systems Assignment 1:
Outcomes? Distributions for: Maximum height layer index number average fitness
Magic number!!
- There is always some magic number turn that you are almost guaranteed to have a safe pass at the turn!!!!
Complex Systems Assignment 1:
Complex Systems Assignment 1:
Complex Systems Assignment 1:
Accordance with the data
Complex Systems Assignment 1:
Playing Jenga is a random walk process!!!!
Real data analysis shows the random walk process by exhibiting Gaussian features in fluctuation plots.
And the magic number emerged…..
Complex Systems Assignment 1:
In the case of the model:
Whoever takes the 7th turn is almost guaranteed a safe pass.
The Toy Model mimics the emergence of stability regions and gives an indication about the gross behavior of the ‘Jenga’ network.
Conclusions
Complex Systems Assignment 1:
Bibliography
Complex Systems Assignment 1: