Tag: Complex Analysis

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.…
Naming Artworks with Help from Bots: From Celestial Arachnid to Ringscape Skyline

In the old days, my digital artworks were numbered:Reality and Imagination #0 to #12. Then I started Atoll of Diffraction and immediately christened each artwork, giving it a title like Peek through the Peaks. It added another interesting step to the creative process! So, I needed to make Reality and Imagination complete as well! After…
Solid and Ethereal. Reality and Imagination.

. 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. . . I am crafting virtual sculptures: with code, I draw structures based on mathematical functions. I got to know these functions when I was learning…
No Loose Ends

I don’t like loose ends. But my physics/math art curves have often been cut off, like fraying fabric. I have tried to let them taper off smoothly, letting them fade in the dark, but I would prefer closed lines. The real and imaginary towers have flat roofs. When using software, I tilt the structures, so…
Imperfect Projections

___________________ _______ __ _ _ __ _______ ___________________ Imperfect Projections dissolve the inherent rectangularity dedifferentiating the materials used dependent on the subjective attitudes create interventions change the landscape of the city with a highlight of the spatial dimension a broad utility as a datum for the objective consideration engineers who are responsible resolve multiple objectives…
Field Lines and Potentials – Reality and Imagination Reloaded

I am creating Physics Art very much like I create Found Poetry. I need tough constraints, silly rules, and tools not designed for art. In a world of perfect renderings and deep fakes, I restrict myself to programming parametric curves. Just lines. There are millions of beautiful parametric functions you could choose from. So, I…
True Colors

I have picked two colors. They shall shine in the dark. ~~~ Another version of my series Reality and Imagination. I used artistic license when tweaking the color values.
Boosted

I have been playing with the geometry of special relativity again! The light cone signifies the invariance of the speed of light. There is a notion of length in four-dimensional spacetime, defined as c2t2 – x2 – y2 – z2. Surfaces of constant length are 4-dimensional hyperboloids. Light rays are null rays, as light travels…
Complex Alien Eclipse

My colorful complex function lived in a universe of white light. I turned off the light. Turned it into its negative. Expected it to look bleak. Like thin white bones on black canvas, cartoon skeletons of imaginary alien creatures. But it is more like the total solar eclipse I watched in 1999. There is interference,…
Spins, Rotations, and the Beauty of Complex Numbers

This is a simple quantum state … |➚> = α|↑> + β|↓> … built from an up |↑> state and a down state |↓>. α and β are complex numbers. The result |➚> is in the middle, oblique. The oblique state is a superposition or the up and down base states. Making a measurement, you…
Lines and Circles

I poked at complex function 1/z, and its real and imaginary parts look like magical towers. When you look at these towers from above or below, you see sections of perfect circles. This is hinting at some underlying simplicity. Using the map 1/z, another complex number – w=1/z – is mapped to z. Four dimensions…
Reality and Imagination

Grey and colorful. Cutting through each other. Chasing each other. Meeting in the center, leaning on each other, forming an infinite line. ~ Reality and Imagination: Real and imaginary part of complex function 1/z: ~ The real part of 1/z is painted in shades of grey, the imaginary part in rainbow colors. Plots are created…
Super Motivational Function

I’ve presented a Motivational Function, a while back. It is infinitely flat at the zero point: all its derivatives are zero there. Yet, it manages to lift its head – as it is not analytic at zero! If you think of it as a function of a complex argument, its weirdness becomes more obvious. Turn…
Motivational Function

Deadly mutants are after us. What can give us hope? This innocuous-looking function is a sublime light in the dark. It proves you can always recover. If your perseverance is infinite. As x tends to zero, the exponent tends to minus infinity. The function’s value at zero tends to zero. It is a zero value…