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The Mandelbrot Set-Part VII: Multibrot Sets | Rhapsody in Numbers
| | beej.us
The Mandelbrot Set
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| | acko.net
How to Fold a Julia Fractal - Acko.net
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| | A tale of numbers that like to turn: a different look at complex numbers and the strange things they do.
| | www.dyalog.com
Beauty and the Beast | Dyalog Blog
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| | [AI summary] The article discusses the creation of ASCII art using the Mandelbrot set with APL programming on a Raspberry Pi, highlighting the mathematical beauty of fractals and their visualization techniques.
| | djalil.chafai.net
A probabilistic proof of the Schoenberg theorem - Libres pensées d'un mathématicien ordinaire
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| This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for...