Feb 6, 2017 · A new kind of companion matrix is introduced, for polynomials of the form c (λ) = λa (λ)b (λ)+c_0, where upper Hessenberg companions are known for the polynomials a (λ) and b (λ). This …

) = c( a( )b( ) + c0 where upper Hessenberg companions are known for the olynomials a( ) and b( ). This construction can generate smaller entries than the Fiedler or Fro enius forms. This generalizes P …

Jan 21, 2025 · Also, I discussed bifurcations that happen on the real slice of the Mandelbrot set: a parabolic bifurcation and a period-doubling bifurcation. On Thursday, I wrote out normal forms for …

Jun 20, 2016 · This construction can generate companion matrices with smaller entries than the Fiedler or Frobenius forms. This generalizes Piers Lawrence's Mandelbrot companion matrix.

The Mandelbrot set within a continuously colored environment The Mandelbrot set (/ ˈmændəlbroʊt, - brɒt /) [1][2] is a two-dimensional set that is defined in the complex plane as the complex numbers for …

The Mandelbrot set, the topic of this notebook, became famous as a simple model which produces extraordinarily complicated (and "beautiful") fractal structures.

This generalizes Piers Lawrence's Mandelbrot companion matrix. We motivate the construction by use of Narayana-Mandelbrot polynomials, which are also new to this paper.