Using logistic maps to define the level of a company’s complexity.

I already shared how we are using the level of Autonomy and Variety in companies to define the level of complexity and the current stage of a company (or group) from four available stages (order, growth, complexity, entropy). In this post, I want to show how you can use certain values of autonomy and variety to determine the company stage.

There are four stages groups continuously move through in endless cycles: Order, Growth, Complexity, & Entropy. To achieve their goals, groups need to be in the correct stage comparing to their environment. Therefore understanding what is your stage and the environment stage has a lot of benefits for companies.

Our approach is based on Logistic Maps. A simple formula that generates immense complexity. The theory is that using this formula we can also map the current level of autonomy and variety to a certain level of complexity. Knowing the level of complexity we’ll have the ability to provide mapping (and formula) that translate different levels of autonomy and variety to the right stage.

Logistic maps are used to depict the growth of a population. I won’t get into the details. All you need to know that one parameter in this formula controls the behavior. This parameter is the growth rate. In the formula, it represents as R. Certain level of R represents different behavior of the system.

If R is less than 1.2, the population will decrease. If R is greater than 1.2 and smaller than 3.2, the population will be stable. If R is bigger than 3.2 and smaller than 3.569 the population will develop repeating periods of different populations. If R is bigger than 3.569 the population will change unpredictably.

Those four options match the four stages (entropy, order, growth, and complexity) we presented in our previous post. We propose to use those R values as known values for each stage. If we create 10 columns and 6 rows table to depict variety and autonomy, the value in the low left cell will be 1.2. The value in the upper left cell will be 3.2. The value on the right upper cell should be any number bigger than 3.569. We choose a value of 4.5. The value in the lower right cell should be any value smaller than 1.2. we choose 0.5.

The logic above defines the stage for four different combinations of variety and complexity, but what with the other options?

To resolve this we used bilinear interpolation to define all the values for all the cells between the four defined cells above. The results can be seen below.

You can use this reference table to find out what is the right stage based on a given value of autonomy and complexity. It’s clear that there aren’t clear stages and each stage is a blend of at least two stages. The gradient colors provide more accurate information on the stage a company or a group is in.

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