I don’t know that an algorithm and a data structure have to be equivalent representations of the same thing to be isomorphic. In the case of the algorithm, is it the code that must be equivalent? Or the runtime behaviour?
The runtime behaviour of the ‘whirling regions’ algorithm clearly is not an equivalent representation of the two-dimensional array representation of an image. However, the runtime behaviour of the quadtree algorithm exactly matches the quadtree data structure.
This is my proposition: That what matters is whether the algorithmic behaviour is equivalent. I would say the same thing about `binrec` matching a binary tree.
...Or at least, I would have, up until today. I am open to being disabused of this notion.
Isomorphic means "have the same shape". It means that there is some structural property that the two objects have in common. The more interesting/complex the property is (and the more superficially different the two objects look), the more defensible the use of the word is.
The runtime behaviour of the ‘whirling regions’ algorithm clearly is not an equivalent representation of the two-dimensional array representation of an image. However, the runtime behaviour of the quadtree algorithm exactly matches the quadtree data structure.
This is my proposition: That what matters is whether the algorithmic behaviour is equivalent. I would say the same thing about `binrec` matching a binary tree.
...Or at least, I would have, up until today. I am open to being disabused of this notion.