Mathematicians discover new fractal structures that defy traditional measurement
Researchers have identified the first examples of mathematical objects with transcendental dimensions—numbers that cannot be expressed through standard equations—within a specific algebraic structure. This breakthrough could have implications for how computer scientists model complex systems and design algorithms for data compression and network optimization.
Originaltitel: The Hausdorff dimension of the generalized Brunner–Sidki–Vieira groups
We compute the Hausdorff dimension of the closure of the generalized Brunner–Sidki–Vieira group acting on the m -adic tree for m\ge 2 , providing the first examples of self-similar topologically finitely generated closed subgroups of transcendental Hausdorff dimension in the group of m -adic automorphisms for m\ge 4 even.