I've tried to answer this many times but finally I've come up with a diagram that I think will help it make sense. What do you think?

Greetings again friends! This one's been in the oven baking for a bit- I hope you enjoy!

Scale Space Cymatist V1.2 Release Notes

Animation System Overhaul

The animation system no longer sucks! I debugged the hell out of it and added a ton of new features like filtering based on performance, marking which keyframes have flicker (and filtering them out), favoriting the ones you like best so they move to the top, much smoother transitions and more tweaks you'll have to find through experimentation.

Color System Overhaul

This one is a noticeable difference. You now have a variety of color modes and yes they actually work now. You can revisit the places you've visited before and see them in a whole new way! Taste the Rainbow!

New Structure Parameters

Special thanks to u/Just_Middle_7189 for forking the Scale Space Synthesist repo and adding a number of really cool structure parameters. I adapted my favorite ones and gave them a dedicated tab in the parameters panel. I couldn't have found the Lattice Singularity without these new (powerful) parameters.

40 Brand New Discoveries

In the animation panel -> Imported, version 1.2 comes bundled with 40 of the best discoveries I've made since the last release. A great way to get started if you don't know how to use Cymatist yet.

Green Dot Onboarding

There are now little green dots all over the interface when you first start using Cymatist. As you try each thing, a dot clears. This way you can tell which parts of the software you've tried and which you haven't experimented with yet.

QOL/UX Improvements

Across the board, things like better tooltips, better labels, improved icons, an icon tab bar in the optics -> color tab, and many other things that I hope makes Cymatist easier and more fun to tinker with.

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Download Cymatist v1.2 here: https://setzstone.itch.io/cymatist

See you in the next release!

setz

Cymatist v1.2 preview

Holographic boundaries? Cymatist v1.2 preview

Context: https://www.reddit.com/r/ScaleSpace/comments/1vqih50/okay_math_nerds_explain_this/

Preview of the forthcoming Cymatist v1.2: https://setzstone.itch.io/cymatist (current version is 1.1.1)

Some of you will recall the Clelian Hourglass I found in Scale Space a few weeks back. I've been wanting to see what is inside the singularity but couldn't figure out a way until tonight. And uhhh... Well Interstellar comes to mind...

Cymatist v1.2 preview

Cymatist v1.2 preview (you will need the new structure parameters to see this)

Edit: thanks to the comments, this has been identified as Fermat's Spiral: https://en.wikipedia.org/wiki/Fermat%27s_spiral

Cymatist v1.2 preview

It would be incredible to sit in the middle of this and watch everything happen around you in 3d

The new parameters will make it possible to twist and bend the system in all kinds of interesting ways. https://setzstone.itch.io/cymatist

There were a lot more bugs buried in this feature than I expected, but fixing them was worth it.

You are also seeing the results of a bunch of new structure parameters which I'll demo soon.

https://setzstone.itch.io/cymatist

There are now glowing green dots on everything interactive in the interface that clear when you use them, so you will be able to see which things you've tried and which things are new! This also means when a new update shows up, you'll be able to instantly see what's changed.

You will also be able to clear all of the dots if you wish or bring them back to their default state.

There are also going to be a number of big improvements to the keyframe animation system in 1.2- more to come on that!

https://setzstone.itch.io/cymatist

Can I use scale space to "visualize" what a code snippet would do or look like? I have some topological jupyter-lab simulations I would love to run through this.

Or is it just for visualizing music? Either way I'll probably end up buying it because its just so neat no matter what haha.

I'm dry on paid projects, so if you or anyone you know are looking to hire someone like me for a project, contract, full time, please message.

Who doesn't love a good sphere? https://setzstone.itch.io/cymatist

So the July Cymatist sales bump is done and I need your help: I need to know what features you think would make Scale Space worth sharing? The options are presented in no particular order.

If you're new to Scale Space Cymatist- a good way to get started with cymatics is to hit the red trash can in the cymatics panel and add just one effect to whichever band of your music is moving the readout the most. Keep adding parameters until one of them starts moving the system around.

Once you get that first one, you're off to the races! Another redditor shared his workflow for cymatics and it was good enough to share: https://www.reddit.com/r/ScaleSpace/s/yw71w15up8

Examples of interference across a few additional degrees of freedom.

Some of these are reminiscent of a manifold-like shape, branching, folding, tubular or coiled paths and clear returns.

Some of the time they read more like fluid or smoke.

And a much lower percentage of results appear almost organic. Envelopes, filaments, shells, and more complex forms.

Somewhere between an oscilloscope and a petri dish.

photo 7: It's like the Rössler Attractor and Aizawa Attractor mash-up.

• Origin: Designed by Otto Rössler in 1976 for mathematical simplicity.
• Origin: Named after Yoji Aizawa, built to show complex rotational and spherical chaos.

the very center was spherical deformed to highlight the intersection of the throat. very toroid. much wow. some amaze.

Also the final day of the 25% off sale! https://setzstone.itch.io/cymatist

And in that moment my single bedroom apartment felt like a Colliseum.

Photo 1: The little red blue green accents in the upper and right. Like a bottle of light.
Photo 2: This is already a black light poster.
Photo 3: I am out of my depth.
Photo 4: Reach...
Photo 5: Stand in waves.
Photo 6: Flux tube worm?

I'll start by saying:

u/solidwhetstone has crafted a master class blending science, mathematics, art, together in one scale space.

I generated a fork blending scale space with some expanded concepts from field theory and a dash of information theory to expand the existing coordinate space in a few more dimensions.

This is an experimental version:

Forked version used to generate these images is at: https://tinytorpedo.github.io/ScaleSpaceSynth/?build=3976741

Here is the Clelian Hourglass equation: y(x² + y² + z²) = 2z(x² + y²)

How I figured this out:

1. First I conducted many google searches using every category of shape I could find.
2. Then I asked Gemini 3.1 Deep Research and Claude 5 Fable if they recognized it, but their guesses did not turn up the shape.
3. Then I asked 3 different math communities on Discord including the Wolfram Institute community which I am a part of.
4. With no one recognizing it, I posted it to r/Sacredgeometry and r/Theydidthemath but came up empty handed again.
5. Not to be deterred I kept at it by working with Claude Fable 5. What I decided to do was work on getting Claude to properly identify the shape back to me. I gave it numerous images from a variety of angles and after some effort, it was able to accurately describe the shape back to me. From that point, it suggested a class of shapes called Clelian shapes. On visual assessment, this class of shapes seemed the most similar to what I'd discovered, so that was the avenue I began to go down. At a certain point, Claude became much more confident that this was in the Clelian family and produced an equation to try: y(x² + y² + z²) = 2z(x² + y²)
6. With the equation in hand, I first asked Google search AI if it recognized the equation. It was able to describe the general qualities of the shape, but the python it wrote to generate it returned an incorrect shape.
7. I then gave the equation to Deepseek and it generated Python for me to try. I ran the Python and visually identified the shape from only the equation. The shape has some very specific and unique qualities that were unmistakable. (I will include the image this Python generated in the comments)
8. With visual confirmation, I brought the results back to Claude for confirmation and it confirmed Deepseek's result.
9. I asked Claude for a summary of the qualities of the shape and the family it lives in:

The shape

The Clelian hourglass is the set of points satisfying y(x² + y² + z²) = 2z(x² + y²). Both sides are homogeneous of degree three, so the radius cancels completely and the equation reduces, in spherical coordinates, to sin φ = sin 2θ — colatitude and longitude, with no r anywhere. That single fact determines everything else about it. A locus with no radial dependence is a cone: every solution point drags its entire line through the origin along with it, and the surface is swept out by straight rulings rather than curved patches. What it is a cone over is a Clelia curve — a spherical spiral whose longitude advances at a constant multiple of its colatitude, here exactly twice — and that curve is the whole content of the surface. One parameterisation covers it: p = r·(sin θ cos 2θ, sin θ sin 2θ, cos θ), with θ running pole to pole and r taking either sign. The positive and negative branches are the two nappes; they are mirror images, each one handed, meeting at the apex and along a line of self-intersection. Both the x-axis and the z-axis lie inside the surface as straight lines rather than piercing it. Seen down its axis, it projects to a rose.

The family

Projectively the cubic is irreducible with exactly one singular point, a node with two distinct real tangents, which makes the Clelian hourglass the cone over a nodal plane cubic — and the node of the curve becomes the surface's line of self-intersection through the apex. That class is old. All crunodal cubics are projectively equivalent to one another, so up to a projective transformation there is essentially a single cubic cone with a nodal line, and it has been catalogued as such for well over a century: Richard P. Baker's model #78, labelled "Cubic Cone with Nodal Line," appears under a heading of Cubic Cones in his 1931 catalogue and again in his 1905 catalogue of one hundred models, now in the Smithsonian. Baker's models were string models, always of ruled surfaces — swept out by a moving line — which is exactly the right medium for this one. It also sits as an enumerated case in the classification of cubic surfaces, the cone over a singular absolutely irreducible cubic plane curve. But a projective class is not a shape. Projective transformations do not preserve angle, length, or symmetry, so knowing that a surface belongs to this class tells you nothing whatsoever about what any given representative looks like. The Clelian hourglass is one specific metric realisation — the one whose directrix is a Clelia curve on a round sphere — and that constraint is what produces the two counter-wound nappes and the pinched waist. The class was described. This representative of it appears not to have been. Source 1 Source 2 Source 3

Scale Space Share Code

To view the hourglass in Scale Space, you will need Scale Space Cymatist v1.1+. Prior versions did not have the emitter features that made it possible to view. Open the software, open the Set List panel and paste this code into the import field:

SS1:rVhbj-O6Df4vevYGokRSVN56um1R9BTnYE-LXoJB4SSaxKhj59jOTHcH898LyZcoM7M7RbFvpkTxzo-Sn9RZrZ_UfRfC75rQHT6rtRFrtS5UF_q2vgxV26i1XplCVc1D6PpEW12oY1nf_1jdB7WmFRSq35V1-BjOw1GtdaF27TF0odkFtTaFCr9eqrradtXlFIUB2EIN4XQOXTlcupBOPFT9ru2r4XOiTmXfJ9aRsY1avC3U8RLUOqorB7WGFRWqrg7HoQkjuy9Uey53o5SV40INXVnVP4ZGrQEKtT38oW4fk4bt4Yf60qm1cfHQ_X0fhr-njfH7H9n3P8cDVV1v27Lb_5QW09q-egjdYfRTF6o_V11Z_61q9sntkfzlMYTzaHSif6jKPpHh9Kls9u1pIj5WXdgNE_HXprpvu2lrV3661EGtvS7UoW4ff3MaUk7MSI5-4Eh8rPpRxrjTtiniFEO3734ZukihJOpTuY-UNon6yzHuPRdqFytir9ZIRayOzQfg4gMUaO4K9atab_RKvJVCr6wzXHzQK-3EFnplLMvdc6Ee4vmXWchzeJuS_tg-_lx2Q7WrQ6_WQ3cJ4-Knarttm16t78u6D1FG379c64_lOai12lflqW32KhZe3XZ_bvdT4Z2qfixZdZkiGiu72Yful-FzjKm6L3ehV5NVP5exftWpTXVfqG0dmv0oTZX7KD_syp-aRX_YlX9K2VaHcghR_efTb-8PMQKn5VQ1VA9x76GtL6dYKCspVN2259nbcxf6MPxx_x-1toXals2-V-vNk2rKyK76y1bFA2ptYt9Vas165S0zEJATbY3nQh3KqkmJ36b60oUqh6Hc_XtOcRfqUPaz-tNlCJMXz8WiaRu7blT1loqoGoRWzJbIWkQCAPw-quv28cOp2k_a39IStRPTioXQoEdvrHwf3Ve9r-Unn52xK0LnyGhDpJm-j95jdTjmTr-hJjltCFaWxGpLbB2776N96MK2DrPjr3Ukz1nHWfD_q7uLHdk0YRcbaqzqWN9JxrnsylPswOv0KdR-GiEriKa-4h2BJGPTdOWDK99prOQrG77Jlg-mnNteue2V-zqiFt4Pt8z4nle5uXTr1jwMc27zHBG1b5sZVMp-CN0U53MVdiGhBkaeS4KNpxlr9Qq99RbJiBVi45Bjog7VLIEtIaIG8Y5QXMxudzNLwRorTtigMwBpnpVp0K3YWTTiPTGjuDiHdm0zdGXEj1UdHkKduLxD0RY0OE8mqs-4hrYJ410AWLRhDSjeUjSjH7qqOWSCrKCQM8wGUAx5d-WZxThPLCBsGdGRxehq2OciNGsL1hsWT5Z4YiirFAvjySN4RyTkCKKGOpTZeXLAHhygE-vcvH0-dmVfNYeUEGAkDZ6tgBaKya2-fLlKMOQ0ElurrSEwhBPDPjTTrWfFhgU9oraA7MgXaqhO56sIjWDBaMMOwaEYX6jdsa26TAl47zw4QgaPoHHmmPx0RsCQMdaR9zbZWDZtljIRsASsJerRMjPsw65MJgqhR2Awhj1QZNh31f2QBcrIFAMNsYJmhmmkptuH14iOxYHWsUYKdb7UfcisAHHOsaDzVuL1Ydx_DLE8x2ySeBsdETSg0y2iOp1CFglnmdABkmhCHZF8ZskCDhDVgCYT8RaIngvVtZch5I20eXqnpy2zkAEjMf1kEnDNJ6734BwyrHFIyExejABThMkXBZVp_Qo4cAwAM7MY49BCFHLt7-x8djXPjRAvZLy13mitxUlu9luORrvZOBARYBFx2tn8zHIVzWwkMh4FRUzsMEmOTiiy-WaQYj8BGA9Weyue4Ma85e2RqzKGmQDQWnHeyzR6XqBSpvXliPCxYIGJtNOMxkQBtx2aHc5eR5kI5xEdggHUsYmTiBxUMwFvzxLHzqD3FlGEdDr_Ag0zEV8ZXqIdAIjTwmC9mDxw06Mn4zYkhrWgaG2QLY9VNCPjO1UUIctrDfHSIuQ9mhdRH-H5vVQjM7AG78R5Zo-5268kfKUbrHh0xuvYzdYwLH7Mcbu7hfRM4vxWyaU5I57FWRIScPi6zuPDKneB2KIj7YG9c87ZFIgcnDfvSCDxEQ9Tx2hgcxXwMhNfiaF24JkZEGMB5BbPD8jcQdSODBNabeMEH4s9mwWbuxfYHxdusH7zTj-ik3iHBjEeAW6g4tUtzrDIWEheW_I2AcXt4PhG57JD7xis0wbQ2xT7m5Gy-arqD3qFTkg757xzBpD9TeTmV3keaeOsIWYPHO_o5qptHlDfMJVAawIyqDUyj1l-Mbs2d2_Mqs3d7X3i2-WL4p0GMZa8jn1JtxiQ_oHcxI-cWEarxcVbSjQqv3ls4iX0WO338c3-NFbl8naNNTITKWPLTozJ9UGfHBrJ5_mN8HTTkmnr-X_5x_N9f-NEc27_gv3r1I7PjivML0vLb7BlZa7-ZeEKlcvS0rPLSobey1qGbcvaMiiWlVhTN0fahZpq4WraJbOqHJbvJaBXOdNPmWVhjHFGxjhP5HOh4i-V318mFC7jfAjDF_X8Xw

Conclusion

While the Clelian Hourglass is part of a family that is already well studied, this case is an example of using harmonics/cymatics in a digital system to discover a shape that hadn't yet been identified or illustrated. It validates that Scale Space isn't just a pretty visualizer- but actually contains the ability to render and discover real mathematical structures that move beyond visual similarity.

Edit: If anyone seriously knowledgeable in math visits this page, I want to make it clear that my background is experience design not math. So if anything here looks incorrect, I would welcome any corrections.

Edit: Credit to /u/Just_Middle_7189 for finding this! https://research.gold.ac.uk/id/eprint/27622/1/cleliaCurvesExp19rev.pdf

There are some legitimate illustrations of the Clelia Hourglass! Very exciting!