Bohemian Matrices

Doubly Companion 19x19
A close up of the fractal pattern for the Bohemian eigenvalues of a sample of 50 million 19x19 $(p=18)$ doubly companion matrices: $$\begin{bmatrix} -\alpha_1 & -\alpha_2 & \cdots & -\alpha_p & -\alpha_{p+1} - \beta_{p+1}\\ 1 & 0 & \cdots & 0 & -\beta_p\\ 0 & 1 & \cdots & 0 & -\beta_{p-1}\\ \vdots & \vdots & \ddots & \vdots & \vdots\\ 0 & 0 & \cdots & 1 & -\beta_1 \end{bmatrix}$$ with $\alpha_k \in \{-1, 1\}$, and $\beta_k \in \{-1, 1\}$. The plot is viewed on [0.95+1.10i, 1.05+1.20i].