Tootfinder

Quantum-Circuit-Based Visual Fractal Image Generation in Qiskit and Analytics
Hillol Biswas
https://arxiv.org/abs/2508.18835 https://arxiv.org/pdf/2508.188…

Quantum-Circuit-Based Visual Fractal Image Generation in Qiskit and Analytics
As nature is ascribed as quantum, the fractals also pose some intriguing appearance which is found in many micro and macro observable entities or phenomena. Fractals show self-similarity across sizes; structures that resemble the entire are revealed when zoomed in. In Quantum systems, the probability density or wavefunction may exhibit recurring interference patterns at various energy or length scales. Fractals are produced by basic iterative rules (such as Mandelbrot or Julia sets), and they p…

Sharkovsky's Ordering in the Mandelbrot Set
Reila Zheng
https://arxiv.org/abs/2506.06163 https://arxiv.org/pdf/2506.06163

Sharkovsky's Ordering in the Mandelbrot Set
Sharkovsky's ordering describes orbit forcing of interval maps, and generalizations of Sharkovsky's ordering exist for maps of trees. In this paper I will describe Sharkovsky's ordering and analogous orderings for trees, and their occurrence on the Mandelbrot set.

Resolving an error with path-tracing and a 2-to-1 mapping in a work of Jang, So, and Marotta
Murali Meyer, Daniel Stoertz, Mike Wang
https://arxiv.org/abs/2508.18543 https://

Resolving an error with path-tracing and a 2-to-1 mapping in a work of Jang, So, and Marotta
We identify two nontrivial errors in the proof of the main results of the work \emph{generalized baby Mandelbrot sets adorned with halos in families of rational maps} by Jang, So, and Marotta. We correct these errors, showing that the main results remain true.

I have spent the evening confirming there's basically no point trying to run code on the 780M iGPU in a Ryzen 7 Pro 8840HS. Like, sure, it works. It runs the Mandelbrot set pretty quickly. Inference? DDR5 memory bandwidth bites hard: might as well just run it on the CPU.

Factorization of the quadratic Misiurewicz-Thurston polynomials
Nicolae Mihalache, Francois Vigneron
https://arxiv.org/abs/2506.17662 https://

Factorization of the quadratic Misiurewicz-Thurston polynomials
This note provides the complete factorization of the Misiurewicz-Thurston polynomial $q_{\ell,n}=p_{\ell+n}(z) - p_\ell(z)$ over $\mathbb{C}$, which plays a central role in the study of the Mandelbrot set, where \[ p_0(z) = 0, \qquad p_{n+1}(z) = p_n(z)^2 + z. \] The roots can be classified into two categories. First, there are hyperbolic points $\operatorname{hyp}(k)$ for any divisor $k$ of $n$, which are parameters whose critical orbits are of exact period $k$. Those are roots of $q_{\ell,n}$…

Recent Progress on Fractal Percolation
Istv\'an Kolossv\'ary, Sascha Troscheit
https://arxiv.org/abs/2508.08150 https://arxiv.org/pdf/2508.08150

Recent Progress on Fractal Percolation
This is a survey paper about the fractal percolation process, also known as Mandelbrot percolation. It is intended to give a general breadth overview of more recent research in the topic, but also includes some of the more classical results, for example related to the connectivity properties. Particular emphasis is put on the dimension theory of the limiting set and also on the geometry of the non-trivial connected components in the supercritical regime. In particular, we show that both the Ass…