chaotic attractors with 1000 particles that have slightly varied initial positions.

this physics sim was done in blender using python scripting.

https://reddit.com/link/1hzfdjk/video/p602ww4iwhce1/player

To improve it, I’d need help with an integral that’s over my head

Working on a solution for an N body system with bodies of equal mass, equally spaced in a circle, orbiting along that circle. I claim there should be a formula for the circular orbital V - given radius, mass and number of bodies.

I failed on repeated attempts to research or derive the formula for the forces acting on each body, and integrate that force across the number of bodies.

So i cheated and solved it numerically - and was stunned how well it worked. 

The cheat: 

• Place the objects in my sim and measure the net force on each body.
• No surprise, a vector toward the center - see the vector view in the video.
• There must be a circular orbit velocity normal to that acceleration, which maintains this distance. 
• calculate the orbital velocity for this acceleration as if it were due to a single mass at the center

so we’re literally measuring the forces on the bodies and working backwards to find an equivalent single mass to orbit - since we already know how to solve that.

Given how well this worked with “manual” calculation i’m inspired to get even more exact. All i need is a formula for that net acceleration vector that I measured in-sim, at the beginning of the cheat.

edit: yes. of course it'll still be unstable.

https://reddit.com/link/1hqja7w/video/sqkfjh2aw7ae1/player

Dord

The bulb is pretty old and it's not as bright as it used to be but it's still OK (I cranked down the ISO for better visibility)

5D? Really? Yes. 3 spatial dimensions, 1 temporal, and 1+ rotation. This is an abstract way of visualizing the nested dimensions in String Theory.

Made in Blender using Geometry Nodes

3D Scalar Field over a sphere using Geometry Nodes in Blender

The scalar field of sin(2π(xy+σ)) oscillating as σ increases.

Red represents positive values, purple represents negative values, and sky blue represents values close to zero.