TODO

[AlexEnrique]

TODO list

• [ ] Implement an algorithm to generate a bifucartion diagram.

  • [x] Make the bifucartion diagram of the logistic family.

• [x] Implement a function to study the stability of fixed points.

• [ ] Implement functions for periodic orbits.

  • [ ] Determine a way to deal with asymptotically periodic orbits.

• [ ] Think about how to get the Lyapunov number/exponent.

• [ ] Design a way to deal with itineraries

• [ ] Start to write the documentation

[AlexEnrique]

• [x] Exclude the opCall() method of the Map(alias f) class.

That method was used to have access to the aliased lambda. One way to get access to the lambda is to define a function template to capture the same alias as

auto foo(alias f, ...)(Map!f map, ...) {
    \\ use 'f' here.
}

[AlexEnrique]

• [x] Start using a implemented function of the phobos or some library to get the derivative of the a function (e.g. in the isSink() and isSource() functions).

[AlexEnrique]

• [ ] Try using the following syntax to allow template alias with dynamic functions (e.g. with probabilistic iterated function system).

map!(x => dynamicFunc(x))

• Is there an way to deal with run-time template values?
  • Possibly Voldemort Types returned by templates?

[AlexEnrique]

Is there an way to deal with run-time template values?

• Possibly Voldemort Types returned by templates?

Yes! Look at this working example:

auto createLogisticMap(double a, real x = real.init) {
    class _LogisticMap : Map!(x => a * x * (1 - x)) {
        this() {}

        this(real x) {
            super(x);
        }
    }

    if (x != real.init) return new _LogisticMap(x);
    return new _LogisticMap;
}

auto rnd = Mt19937_64(unpredictableSeed!ulong);
auto map = createLogisticMap(a, rnd.uniform01);

• [x] Implement it!

[AlexEnrique]

if (x != real.init) return new _LogisticMap(x);
    return new _LogisticMap;

• The possibility to return a map without initialization asks for a kind of .setInitialValue() method of the Map!(alias f) class.
• [ ] Resolve this issue.

[AlexEnrique]

• [ ] Change the type of _orbit member variable to Appender!type