Suppose I have a root finding method on some function on the complex plane , okay, that gets us partitioned into Wada basins, and more to the point, those basins are associated with particular roots of . Which means that if a basin is associated with the root , then .
Adding things that go to zero is a good way of making new functions. What if we were to take the sequence generated by the Newton’s method iteration and then add together ? (or any other root-finding method.
for w(z) = 1-z^7, this gets us:
If a root finding method is a rhizogeny, then I’m going to call the class of functions generated this way metarhizogenous.