Come Along

Day 108

Parker_Barbara_1You already know this by now, but I’m from the Seattle area.  So when Justin Valente posted on SoundCloud something called “Hendrix Jam” ( I was inclined to listen, adding to the fact that anytime Justin posts, I hit “Play” and “Download” at almost exactly the same time.  He is a wonderful guitarist who makes the blues cry and sing…love it.  But this purely rock session is Hendrix stripped down to the essence of what made his music so astounding and enduring.  It was a great listen that got me out of the house and into the studio…totally inspired to ‘touch the sky.’  In fact, the resulting painting is part of a new series called “Elements” and is called, simply, ‘Sky’.  I was happy enough with it that it is already hanging in a gallery show – barely dry, but dry enough 🙂 

Strange, in a way, that the evolving guitar is a result of searching through the old barn for creative materials.  I came across tow chains that hang out there for months without use, but every once in a great while are just the thing needed to handle and emergency.  I can’t say that needing a guitar is much of an emergency, but there are days when it feels like it might be.

108_365 Guitars

Chain Gang


Now, one more thing.  My friend Bill sent me the math guitar which is something that just gives me so much joy, so much hope, so much true appreciation for the left brained people of the world – I’d never heard of the Mandelbrot Set – which, considering that it is fractal geometry, is not surprising.  Wikipedia defines the Mandelbrot Set as:

The Mandelbrot set M is defined by a family of complex quadratic polynomials

P_c:\mathbb C\to\mathbb C

given by

P_c: z\mapsto z^2 + c,

where c is a complex parameter. For each c, one considers the behavior of the sequence

(0, P_c(0), P_c(P_c(0)), P_c(P_c(P_c(0))), \ldots)

obtained by iterating P_c(z) starting at critical point z = 0, which either escapes to infinity or stays within a disk of some finite radius. The Mandelbrot set is defined as the set of all points c such that the above sequence does not escape to infinity.

A mathematician’s depiction of the Mandelbrot set M. A point c is coloured black if it belongs to the set, and white if not. Re[c] and Im[c] denote the real and imaginary parts of c, respectively.

More formally, if P_c^n(z) denotes the nth iterate of P_c(z) (i.e. P_c(z) composed with itself n times), the Mandelbrot set is the subset of the complex planegiven by

M = \left\{c\in \mathbb C : \exists s\in \mathbb R, \forall n\in \mathbb N, |P_c^n(0)| \le s \right\}.

As explained below, it is in fact possible to simplify this definition by taking s=2.

Mathematically, the Mandelbrot set is just a set of complex numbers. A given complex number c either belongs to M or it does not. A picture of the Mandelbrot set can be made by colouring all the points c which belong to M black, and all other points white. The more colourful pictures usually seen are generated by colouring points not in the set according to how quickly or slowly the sequence |P_c^n(0)| diverges to infinity. See the section on computer drawings below for more details.

The Mandelbrot set can also be defined as the connectedness locus of the family of polynomials P_c(z). That is, it is the subset of the complex plane consisting of those parameters c for which the Julia set of P_c is connected.

Mandelbrot Set

OK, so you have that, right?  More importantly to me, as Bill pointed out, may be the fact that regardless of the number of pixels in a Mandelbrot image, you can very, very often find a guitar.  Or, as I discovered – the left brain in color…  There are a mess of these, each weirder and more beautiful than the last.  Oddly perfect for the whole Hendrix vibe…Mandelbrot


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