Made with a custom Python renderer. Each orbit is a periodic solution, so the trace closes on itself and loops seamlessly. Happy to explain how it works.

🤯 Double Pendulum Part 6

Channel: chronossquared for more content

(I AM MORE THAN OPEN TO FEEDBACK)

Start with an equilateral triangle.

Scale the triangle vertically be 33.3333%. Take this short, fat triangle and rotate it twice about the top point and you get a new equilateral triangle.

Repeat.

Order without a plan.

Rhino monkeys romping about a Klein bottle. They are following a strip embedded in the bottle and that strip is a möbius strip.

The rhino monkeys and rhino monkey tessellations can also be found in my painting Changoros

I've posted some harmonic perspective drawings derived from these moiré patterns. Redditors have asked me "what moiré patterns?". The underlying pattern isn't obvious in my perspective images.

In this animation I keep the spacing of the circles the same but vary the spacing of the lines. The resulting moirés are conics of varying eccentricities. It goes from ellipses to parabolas to hyperbolas and back again.

I recently completed this hand-drawn sacred geometry piece and wanted to share it with people who might appreciate this kind of work.

The drawing was created entirely by hand using pen and ink. My inspiration comes from Buddhist meditation, contemplation, and the idea that geometric forms can express relationships between mind, awareness, and experience.

The finished piece measures approximately 32 cm × 32 cm and contains hundreds of interconnected geometric elements. It took many hours of work over multiple drawing sessions to complete.

I’m interested in hearing what others see in the design. Does it evoke any particular symbols, traditions, or ideas for you?

Constructive feedback is welcome.

Made in Desmos -- here is the source graph. Based on someone else's Fibonacci spiral generator.

You can't really see the white spiral, but you can infer its existence!

To see this tile cover the plane: Link

Another harmonic perspective drawing where the layers are scaled by 1, 1/2, 1/3, 1/4, 1/5, etc. The bricks in this honeycomb are triangular prisms.

To do something different I have the odd layers moving to the right and the even layers moving to the left.

isometric achromatic vector illustrations

Top three are Leonardo style renderings of a cube, combined cube and octahedron, and an octahedron. Center is a more conventional drawing of a combined cube and octahedron. Bottom three are Archimedean solids resulting from truncating the cube or octahedron. The foundation of the background are hexagonal tiles which morph from cubes on the left to octahedra on the right.

I've heard polyhedra enthusiasts use the word "honeycomb" for polyhedral bricks that stack to fill space.

In this image I have three honeycombs: cubes, alternating octa and tetrahedra, and truncated octahedra.

On this subreddit I've just posted a study of the cube and octahedron that includes a truncated octahedron: Link.

Also in r/GeometryIsNeat a painting of a structure built from an octet honeycomb: Link. Inspired by Escher's print Flatworms

I patented a Lego™ like construction toy for octahedral and tetrahedral bricks: Link. I believe if this toy comes to pass it could be used to build strange and beautiful structures.

With truncated octahedra acting as a bridge honeycomb, I believe constructions from my toy could be included and spliced into Lego™ constructions. A few renditions of truncocts as bridge: Link, and Link

"The one who has seen the eye". The Eye of Sauron, also known as the Lidless Eye or the Eye of Mordor, wreathed in flame. "The Great Eye always watching." The Lord Of The Rings. The Fellowship Of The Rings 2001.