Not exactly, Newton's fractal, which is topological, specifically the wada property, is a boundary condition. It relates to fractal (non-integer) dimensions, w

Not exactly, Newton's fractal, which is topological, specifically the wada property, is a boundary condition. It relates to fractal (non-integer) dimensions, which was first described by Mandelbrot in a paper about self similarity. Here is a paper that covers some of that. https://www.minvydasragulskis.com/sites/default/files/publications/ND_2017_v2.pdf https://www.minvydasragulskis.com/sites/default/files/public... In Newton's fractal, no matter how small a circle you can draw, your circle will either contain one root or all the roots. The basins that contain one root are open sets that share a boundary set. Even if you could have perfect information and precision this property holds. This means any change in initial conditions that crosses a boundary will be indeterminate. There is another feature called riddled basins, where every point is arbitrarily close to other basins. This is another situation where even with perfect information and unlimited precision a perturbations would be indeterminate. A positive Laponov exponent which isn't sufficient to prove chaos, but is always positive in the presence of chaos may even be 0 or negative in the above situations. Take the typical predator prey model and add fear and refuge and you hit the riddled basins. Stack four reflective balls in a pyramid and shine different color lights in two sides and you will see the Wada property. Neither of those problems are addressable with the assumption of deterministic effects with finite precision.