Logistic

Arduino library to explore the logistic formula. (chaos, bifurcation)

Description

The logistic function is a function known from the chaos theories. It represents a model of e.g. how fast a rabbits reproduce and other processes.

The basic function is pretty simple

//  reproductionRate R = 0.0 - 4.0
//  in == 0.0 - 1.0  (think percentage of some maximum population)
out = reproductionRate * in * (1 - in);

For values of reproductionRate R

• below 1 the function stabilizes goes to 0
• between 1 and 3 the function stabilizes after a few dozen iterations.
• between 3 and ~3.57 the stabilization jumps between 2, 4, 8 values (called bifucation)
  • see around R == { 3, 3.45, 3.54, 3.56, 3.57}
• above 3.57 the function turns to chaos with some stability zones. At least visually.

There are a lot of (mathematical) interesting aspects to be found in the functions behaviour.

If you have ideas (or links) to that should be in this library, please open an issue.

Related

• https://en.wikipedia.org/wiki/Logistic_map
• https://en.wikipedia.org/wiki/Feigenbaum_constants
• https://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/BD.html

Interface

#include "Logistic.h"

• Logistic(float rate = 2.0, float in = 0.5) Constructor
  • rate = reproduction rate = 0.0 - 4.0
  • in = input population = 0.0 - 1.0
• void setRate(float rate) set / change the reproduction rate.
• float getRate() get the current rate.
• float iterate(float in) make one iteration given a start value.
• float iterate() make an iteration with the last calculated value.

Future

Must

• improve documentation.
  • related links (youtube?)
• add examples

Should

• Look for other "logistic functions"
• elaborate the library
  • stable() checks delta between previous and current value.
  • period() tries to find a repeating period in the values?
  • count() iteration counter.

Could

• add unit tests
• add graphics? => user task?

Wont

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Thank you,