Apologia for Intuition: Mathematical or Visual

Convergence:

Notes on the Function

Assume there is a function, F_n

Suppose that this function is a single artist, Aprille Best Glover and that this function or artist produces or extracts from the environment a set of artifacts or characteristica for each day n.
Where n = 1 = June 29, 2003 until n = Santiago and each n represents a consecutive day.


Principle Note: the function agrees in advance to use no global rule or model which would set global limits the set of artifacts produced for every day n. Hopefully, precluding a forced convergence.

Note: n = Santiago is an open yet finite number. Open because the precise quantity of days necessary to arrive in Santiago, Spain is not known in advance. Finite. Because baring unexpected death or injury artist will arrive in Santiago in a countable number of days.

Note: Convergence can ultimately be accessed only when n is greater than Santiago.


Lets model this function using a loose version of an active walker model.

F(n) = Walker rule(n) + Stepping Rule(n) +Land rule(n) +Landscaping rule

Each of the four rules is subject to change for each day n.