Tuesday, April 16, 2019

The Model Thinker #14 : Local Interaction Models

Today's installation is so abstract that I will just describe two local interaction models.

First the Local Majority Model :

1 2 3
4 C 5
6 7 8

Each cell in a two-dimensional square can be in two states : White or Black. In each period, one cell is chosen. If a cell is chosen it will adopt a new state if five or more of its neighbours are in that state, otherwise it maintains it current state.

If we allow this Local Majority Model to run over a canvas of Black and White Squares, we will eventually have patches of Black and White like a Holstein Cow.

Image result for Holstein cow

The moral of the story is that where local coordination takes place, the global configuration would be patchy and diverse. This model explains animal hides like that of the zebra.

The Game of Life is more complicated. Suppose we play by these two rules instead and refreshed each cell every period :

Life Rule : A black cell with exactly three white cells turns white.
Dead Rule : A white cell with fewer than two or more than three white neighbours die and turn black.

Depending on the initial arrangement of white and black squares, we will get equilibrium, moving or complex arrangement of black cells. This shows that by just a few simple rules, highly complex functions may result.

Image result for game of life local interaction model

This would be fun if I were still a Computing A level student and programming in Pascal.

But right now, I have no idea how to make this relevant for investors.

Maybe a reader can do some Googling and let me know how he would apply this to making money.

1 comment:

  1. Interaction models = infection = danger of groupthink.

    Like sentiment, markets are usually right in the middle and wrong at the extremes.

    But during the bear or bull process, sentiments & markets will be right. You can throw darts at stock charts to short or long respectively, and you'll make money.

    The opposite happens when the bottoming or topping process is in.