Reality and Imagination

Reality and Imagination is a series of thirteen images generated by custom, hand-crafted computer code. Each image shows the same virtual sculpture from a different viewpoint. I call it virtual as its shape is solely defined by a mathematical function – an object existing in the human mind, in the platonic realm of ideal objects.

This is a retrospective: I have converted a former WordPress Page (created in 2024 and amended often) to a blog post.

It has been my first series using (virtual) metallic tubes, and the only creation of mine that has ever been exhibited.

Each tube is a contour line – a path of constant height above a base plane – following a surface defined by a mathematical function.

~

~

These images have been created with custom, hand-crafted JavaScript code, using the framework threejs (No AI involved).

The images shown on this web page and elsewhere on the internet are low resolution versions. The original images are 9000 pixels wide.

~

Leaning on each other. Cutting through each other.

Two towers are floating through empty space.

Infinitely elongated bells.

Delicate metal tubes.

Tubular Bells.

Forming rings.

Ethereal, yet solid

~

With code, I am drawing structures based on mathematical functions. I got to know these functions when I was learning physics. Now I wanted to explore them in a way detached from any sense of usefulness, trying to make their beauty explicit.

Originally, I built sculptures from plain lines without thickness or depth But I had always envisaged them as made from wire loops or metallic pipes. Finally, I am depicting them as such!

Using my space probe, I am viewing the floating towers from different perspectives. Zooming in and out. Orbiting until I become dizzy. Marveling at the unwordly allure of stacked rings. Detecting twists and turns, spotting the uncanny in the mundane.

Finding elements of surprise mirrors my joyous reviving and relearning classical physics over and over. The allegedly elementary sparkles and glitters, if viewed from the right vantage point.

~

Reality and Imagination is made from real and imaginary part of complex function 1/z. Stacked circles of wires forming tower-like structures. Gold is the color of reality. Blue is the color of imagination.

If z is expressed as x + iy, real and imaginary parts of 1/z are obtained by multiplying nominator and denominator by x – iy. Moving away from the zero point, the denominator x² + y² finally wins, and both parts become zero. Denominators are x for the real part and -y for the imaginary part. At the zero point, the denominator goes to zero faster than the nominators, thus both parts have poles. As x and -y change sign when the zero point is crossed, each function is made up of two infinite towers, one extending to infinity, the other to minus infinity.

The asymmetric towers lean on each other, they meet in the vertical line erected at the zero point. x and -y are π/2 apart, speaking of them in terms of the complex plane. They chase each other, one lagging by π/2, like current and voltage in a resonant circuit, like force and amplitude of an oscillation.

~

Related blog posts and more math and physics background:

elkement’s Art Is Part of the Mathematical Art Digital Exhibition at Queens College, New York! Four images of this series are on display at the math department of Queens College and on the exhibition website.

Reality and Imagination – for Real! Drawing the functions on paper for the first time, using traditional techniques of descriptive geometry – and a lot less contour lines.

Solid and Ethereal. Reality and Imagination. The original presentation of the series, intertwined with personal poetry-like notes. Trying to convey my motivation to create this series and mathematical / physics-inspired art in general. Reality and Imagination marked perhaps the point of time my own motivation to create this type of art became clear to myself.

Field Lines and Potentials – Reality and Imagination Reloaded. A simple and sparse version used as a scientific visualization. Real and imaginary part of 1/z are introduced as holomorphic functions – in the way this is typical done in theoretical physics courses on electromagnetism. Either real or imaginary part represents field lines of some electrostatic field, and the other part encapsulates the electrostatic potential.

No Loose Ends. The same towers, but now explored not via their circular contour lines (of constant height), but by using the paths corresponding to circles “on the ground”. These curves are closed to, but you move and down on the towers’ surfaces.

Imperfect Projections. A study / sketch of half of one such tower, done as fully freehand digital drawing. Creating the orthographic projection from the views from the top and from the side.

True Colors. Re-creating the original images, but now with colors close to Ukraine’s national colors, and on dark background. Created on February 24, 2022.

Reality and Imagination. How it all began. First exploration with real and imaginary part of 1/z, using SageMath. Contrasting grey reality with colorful imagination.

~