Papers › A Fractal Eigenvector
A Fractal Eigenvector
Neil J. Calkin, Eunice Y. S. Chan, Robert M. Corless, David J. Jeffrey, Piers W. Lawrence
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The recursively-constructed family of Mandelbrot matrices Mₙ for n=1, $2$, … have nonnegative entries (indeed just $0$ and $1$, so each Mₙ can be called a binary matrix) and have eigenvalues whose negatives -λ= c give periodic orbits under the Mandelbrot iteration, namely zₖ = zₖ₋₁²+c with z₀=0, and are thus contained in the Mandelbrot set. By the Perron--Frobenius theorem, the matrices Mₙ have a dominant real positive eigenvalue, which we call ρₙ. This article examines the eigenvector belonging to that dominant eigenvalue and its fractal-like structure, and similarly examines (with less success) the dominant singular vectors of Mₙ from the singular value decomposition.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections