The Apeirographic Explorations by Aggott Hönsch István

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An infinitude of Buddhabrot-like pareidolic figures lurk in the hinterlands of the Mandelbrot set:
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Artist Statement & Bio

Aggott Hönsch István I was born in Hungary and spent my formative years in Szentendre, a vibrant cultural centre near the Hungarian capital, immigrating to Canada in the 90s. These days, I live and work in Toronto, based in my North York apartment that doubles as my art/programming studio.

My approach to art is inseparably intellectual and spiritual at once. I am captivated by the improbable marvels hidden within mathematics, and hungrily scour the complex plane in search of more and more curiously aesthetic revelations--knowing they've been waiting for someone to find them since before time was time. In each piece forcefully reified by computer code and canvas, I see order, organization, and an undeniably anthropic conception of beauty that whispers of the divine.

Aggott Hönsch István

About Apeirography

The Wonders of Mathematics

Mathematical realism0 recognizes that numbers are not merely human ideas, but, rather, formless phantom things: eternal, immutable, immaterial—not of this world.

They are repositories of mysteries that prove unreasonably effective at rendering the physical world comprehensible; and their myriad properties—some simple, others intricate—find varied purposes in fields as disparate as astronomy, engineering, cryptography, and, yes, even art.

The way some artists generate algorithmic art can be likened to a process distantly akin to painting, where, instead of a brush, a complex software tool is configured to render the desired strokes to form an aesthetically pleasing outcome, then the results are often further touched up by knowing hands.

This is not the process that created the works featured herein.

Timeless Art on the Complex Plane

Some numbers like \(\pi\) and \(e\) are weird and wondrous in their own way, but there are far stranger numbers out there. Accepting the possibility that the impossible equation \(\sqrt{-1}\)1 can actually yield a sensible result, gives us the imaginary unit \(i\), and the imaginary numbers built thereupon.

These imaginary numbers, while unorthodox, are no less suitable for calculation than real numbers. Indeed, with an additional leap of logic, one can perceive plain integers and all other real numbers as also having a null imaginary component alongside their real parts, and vice versa: thus \(6.29\) and \(5i\) are the same as \((6.29, 0i)\) and \((0, 5i)\).

Illustration of a Point on the Complex Plane, created by Wolfkeeper at Of course, once we have a joined but irreducable pair of numbers—one real and one imaginary—the number line from our elementary school days can no longer bear the strain, and must extend vertically as well; becoming an idealized artist's canvas, an infinite complex plane, whereupon these and all other bipartite complex numbers can reside. And on this plane lies timeless art that predates humanity and the world itself, just waiting to be discovered.

The Art and Science of Apeirography

The reification (whether visual, auditory, or otherwise) of these often inexplicably æsthetic preternatural forms—fractals and other mathematical objects of varying dimensionality that are nothing like the sterile shapes taught in elementary classes on geometry—is the art and science of apeirography; from the greek ἄπειρος /ápeiros/, meaning "infinite, boundless", and γράφειν /gráphein/, meaning "to draw, to write".

And while technically any mathematical visualization can be termed an apeirograph, popular mathematical art today tends toward works produced via third-party software that is necessarily limited to the original programmer's or programming team's considerations, in spite of a wealth of visualizations, presets, and configuration options.

Such programs can produce striking images rather easily, but ultimately the arbitrary limitations and the degree of abstraction between the mathematical object and the artist often makes for results that can seem derivative of the myriad other similarly produced works.

There is, I believe, a better way.

Apeirographic Authenticity

When apeirography is undertaken by an artist who can, at once, be a mathematician, a programmer, and a visual artist, they can—in recognition of the awe-inspiring temporal and spatial infinities and fundamental apartness of mathematical objects—prioritize authenticity of representation. In order to do so, they work closely with the mathematics, write their own programs, and pursue interpretive post-processing with only the lightest touch—not unlike a good photographer wishing to be faithful to their subject.

Such had been my approach to the generation of apeirographic images from the beginnings. Never content with finding mere unexplored byways of widely studied algorithms and visualizations, I wrote one custom program after another, eventually discovering new vistas both by way of algorithms and visualizations.

My apeirograph generators now number in the hundreds: some extraordinarily productive, capable of producing a legion of stylistically unique but distinctive images, or striking video installations; while others of equal or greater algorithmic complexity yield but a single two-dimensional image, often still well-worth the time taken to discover it.

If you enjoy these timeless works and share my awe and wonder that such beauty should be hidden in the fabric of mathematics, please support my explorations and order a canvas print, a giclée reproduction, or an arithmikon wood print.

  1. Espoused by Paul Erdős and Kurt Gödel, among other mathematicians.
  2. No real number, when multiplied by itself, yields \(-1\), because \(\sqrt{1} = \pm 1\) and therefore both \(1 \times 1 = 1\) and \(-1 \times -1 = 1\).

© 2014–2016 AGGOTT HÖNSCH István