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

The logistic library is written for educational purposes.

The logistic function is a function known from the chaos theories. It represents a model of e.g. how fast 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 and 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 bifurcation)
  • 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.

All floats are replaced by double to increase precision. This affects performance and can relative easy be undone by a global replace.

• 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

#include "Logistic.h"

• Logistic(double rate = 2.0, double in = 0.5) Constructor
  • rate = reproduction rate = 0.0 - 4.0
  • in = input population = 0.0 - 1.0

• void setRate(double rate) set / change the reproduction rate. Note this can be changed run-time.
• double getRate() get the current rate.
• double iterate(double in) make one iteration given a (new) start value.
• double iterate() make an iteration with the last calculated value.

• void setCount(uint32_t count = 0) reset iteration counter to start value. Default this is zero.
• uint32_t getCount() returns iteration counter.
• double getDelta() returns the delta between last and previous value.
• double getPrevious() returns the previous value.
• bool isStable(double epsilon = 0.0) returns true if last delta is smaller than epsilon.

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

• Look for other "logistic functions"

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

• add period() tries to find a repeating period in the values?
  • can take too long, especially as double => user task

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Thank you,