We have some function $f(n)$ which yields positive integer values and is defined for integer n.
Example A
We have a x-y-plane and start at $(0,0)$.
We will paint an image on the plane by drawing from the past point a new 1-unit line in a $$\dfrac{360}{N} \cdot (f(x) \mod N)$$ degrees angle.
Example B
We have a x-y-plane with squares and color $(0,0)$ black.
Depending on the value of $$\dfrac{360}{4} \cdot (f(x) \mod 4)$$ we paint the upper, lower, left or right square black and start from this square again, so that another image is created.
Self generated example, where the direction depends on the last digit of the next prime: HERE
In what field of mathematics do we investigate such images/graphs/paths/maps?
I have been thinking whether
- topology or
- random walk theory or
- graph theory
investigates such images/graphs/paths/maps (?), but those paths are neither random nor is this a actual graph.
Dynamics, in particular (or in general, depending on your interests) iterated function systems. See the related wikipedia page.