## Journey of a Ring Along a Penrose Triangle

A neat animated tribar! It’s worth noting that the tribar, or Penrose triangle (aka Reutersvärd triangle), attributed to British mathematician Roger Penrose, was not technically ‘invented’ or ‘discovered’ by him. The geometric principles underlying its existence were already evident in Greek and Arabic ornamentation, including tiling and friezes…

## Apparent size ≠ Real size

Simple demonstration of apparent size and distance… See how the color rings (annuli, in mathematical language) fit snugly.

## Nested Penrose Triangles

This is an illusory geometric structure that cannot exist in our 3D world. Let’s Explore its captivating depths and intrigue.

Here’s how to create this impossible structure. Start by drawing two parallel lines spaced apart from each other and divide them into 7 equally spaced lines.

Then follow the visual steps A, B, C, and D illustrated below. At the beginning (fig. A), you will need to replicate the alignment of the 9 parallel lines three times while applying a 60-degree rotation to each one, finally arranging them to form a triangle. Subsequently, follow the visual directions in B and C to obtain the figure shown in fig. D.

At last, you can add color and gradients to the structure as illustrated below.

Discover prints and merchandise featuring this op art masterpiece at my online gallery

## Ship in a Klein Bottle

Embarking on a journey in a Klein bottle? Absolutely. A Klein bottle is a mind-bending non-orientable surface, defying the usual inside-outside norms. Technically, the ship’s navigating the interior…

## Illusion vs Reality

“Illusion, a derivative of reality, and vice versa.” – GS

For a little backstory… one day, a follower threw me a curveball: ‘What separates illusion from reality?’ I countered with a snap response: ‘What separates acceleration from speed?’

## Perception in Motion: Illusion, Confusion, and Zen Insight

Many perceive the two 3D cross-like shapes as moving significantly, though they remain stationary!

The interplay of color shades (light/dark) on the edges and body of the cross-like wire frames creates the illusion of motion. The alternating shadings simulate “motion blur,” leading some researchers to attribute these illusory movements to delays in luminance processing, producing a signal that deceives the motion system and induces “kinetopsia” (motion perception)..

This brings to mind an anecdote: Two Zen monks debated a flag moved by the wind. One claimed, ‘The flag is moving…’ while the other countered, ‘The wind is moving!’ The monastery’s prior intervened, stating, ‘Not the wind, not the flag; the mind is moving…’

This short anecdote serves to explain that the concept and perception of motion is sometimes ambiguous.

## Autokinetic Illusion

Immerse yourself in the mesmerizing experience as blue droplets seemingly sway gracefully, creating an illusion of gentle motion. The yellow horizontal lines contribute to a wave-like dance, enhancing the visual allure.

This op art piece embodies a peripheral drift illusion (PDI), wherein a sawtooth luminance grating in the visual periphery induces the illusion of movement.

Fascinatingly, studies by vision researchers reveal that the illusory motion activates brain regions akin to those triggered by actual movement.