![](data/eq1.png)
(4) We move g(n) units in this direction and repeat the process.
This process can be summarized through the recursion
![](data/eq2.png)
The walk is generated by adding steps, which may be represented as vectors.
The recursion yields for the position (x,y) at a given moment n
![](data/eq3.png)
The hole walk is therefore given by W(f,g,N). Fascinating patterns emerge very quickly, e.g. by applying f(n) = n. But also a variety of challenges and research opportunities arises when explaining patterns, predicting walks, describing walks as curves or investigating further properties.