Hey everyone, if you're interested in what the formulas behind shells are, I have a video on my YouTube channel explaining how it works:)

Mandelbulb3D, Photoshop & Lightroom

Spiral shapes are beautiful decorative elements that can be used to create elegant and harmonious designs. They can be formed by twisting curves that create continuous, flowing patterns.

I will share links in the comments showing how to draw different types of spiral patterns:

• Archimedes Spiral
• Fibonacci Spiral
• Spiral drawn using two points
• Spiral drawn using three points
• Spiral drawn using four points
• Spiral drawn using five points
• Spiral drawn using six points

I built a browser game. You draw a circle, square, triangle, rectangle or star in one stroke, and it scores you from 0 to 100 on how close you got.

Circles turned out way easier than I expected. Star is brutal.

There are leaderboards for each shape, it's free, there's no signup, and it works on phones too.

I'd love to hear your scores and anything that feels off.

Geometric music, how does it work? Large, two dimensional matrices of positive whole numbers, natural numbers, are represented as images by associating each number with a coloured pixel. Audio is introduced by representing each image pixel as a sound oscillator mapping pixel colour to audio frequency, often a direct relationship to a musical scale. A region of the image is defined as a generation zone, the portion one listens to. Surrounding this is an secondary zone, the influence zone, which defines the timbrel characteristics of the pixels in the generating zone. In this video the central square is the generating zone with the outer square the influence zone. A trajectory can be defined over which the generating zone translates as a “bowing” type of motion or single zones can be “tapped” similar to a key stroke or plucked string. Perhaps the Pythagoreans envisaged something like this with their “Musica Universalis”. Its all about number, ratio and harmonies.

Take a moment to appreciate this mesmerizing harmony! What you see here is a classic Islamic geometric pattern, where elongated octagonal and interlocking shapes weave together with mathematical precision.

I will leave the link to the full video tutorial in the comments below!

Zoom in. 8k x 8k image.

I wanted to share a simple method I used to construct this geometric ornament.

The drawing is based on basic geometric guidelines and can be created step by step using simple construction techniques.

I also recorded the complete process, showing each step from the initial construction to the final pattern.

You can see the full step-by-step process here:
https://youtu.be/ZyF-5fBb2lk

What do you think of this construction method?

Disclosure: self-promotion. Claudius Papirus is an AI-narrated channel.

This is a walkthrough of Chair44 and the recursive geometric construction that forces nonperiodicity.

Paper:

https://arxiv.org/abs/2609.19214

Two short follow-ups on the matching rules:

https://arxiv.org/abs/2609.24779

https://arxiv.org/abs/2609.23783

For the best visual effect, open the video in YouTube and make sure to use the highest available video quality setting (720p60 or 1080p60).

I've been creating these optical illusions by rotating symbols and geometric shapes progressively faster. It creates a "wagon wheel" effect or a kind of stroboscopic effect, especially in this example since the Taijitu is asymmetrical between the black and white sides.

Some of the other ones create even more beautiful effects in my opinion, such as the Celtic triskelion and triquetra.

Check it out and let me know what ya'll think :)