Introducing The Limit of Possibility! Following my popular Enigma Tower and niche Zelda tribute, my latest work celebrates the beauty of mathematics & physics at their limits!

This is my first time using a ring-shaped magnet for passive stabilization. Not only does it make assembly easier, but it also achieves a more consistent / stronger balance. As always with magnets, please heed safety warnings (see below). Also a BIG THANKS to TBone_427120 for publishing how to print a Sierpiński fractal pyramid in spiral vase mode. The settings he published reduce the diamond’s weight by ~33% - key to achieving balance.

Also check out my full Passive Magnetic Stabilization collection (including the latest one: The Explorer's Arcanum) as well as my accidental / surprisingly satisfying fidget, The ClackStack (a set of stackable magnetic weights I created to originally calibrate The Limit of Possibility). While there, I hope you watch the Apple commercial parody I spent a bit too much time creating :D

Limits → Possibilities

1. Size Limit: The unlikely balance of this sizable diamond is at the limit of the passive stabilization I’ve been able to achieve with consumer-grade neodymium magnets.

    

2. Recursive Limit: A Sierpiński diamond’s volume trends to 0 as the levels of recursion increase. This infinite limit is mathematically depicted on the diamond’s tip.

    

3. Earnshaw’s Limit: While this diamond represents 5 levels of recursion (so no, it sadly isn’t completely weightless), its light weight from recursive hollowing is what allowed me to stabilize this sizeable object in a way which almost appears like it’s going to float away. That said, Earnshaw’s Theorem states that stable static levitation using permanent magnets (without active stabilization) is impossible, so full free-floating remains beyond the limit of possibility.

    

4. Manifestation Limit: The base of this model is an inverse Sierpiński object. Think regular Sierpiński, but then make the hollow parts solid and vice versa. This solid base represents the tangible, whereas the hollow diamond represents the ethereal. Where do they intersect?  Where ideas manifest into reality - at the limit of the possible.

At the end of the day, this sculpture stands proudly in defiance of its limitations to showcase what is in fact possible. The Limit of POSSIBILITY.

Required Materials

Most generic magnets are unlikely to have the precise strength required to achieve proper balance - I've tried and had comically bad outcomes! Please use the Bill of Materials magnet links for best results and to support me - thank you!

1. One (1) 10x4x3 mm ring-shaped neodymium magnet from Maker’s Supply (see Bill of Materials).
2. Four (4) 4×2 mm round neodymium magnets from Maker’s Supply (see Bill of Materials – 1 pack is sufficient). If you don’t already have a magnet insertion tool, you’ll need two additional 4x2 mm magnets (total of 6) to create one, but either way 1 Maker’s Supply pack is sufficient.
3. Ten (10) 25×3 mm round neodymium magnets from Maker’s Supply (see Bill of Materials – 1 pack is sufficient).
4. Super glue to assemble the diamond.
5. (Optional) A magnet insertion tool such as the simple one I created. If you choose not to use one, you'll need another way to distinguish relative polarity. Determining which end is absolute N isn't required, but you must be consistent about which end you consider N. You can always use another magnet to assess polarity, though it's easy to lose track of its orientation if it's unlabeled. An insertion tool is a quick print which can save you a headache.
6. (Optional) Stainless steel nozzle – this type of nozzle doesn't attract magnets. But if you monitor the print for the next few layers after inserting the magnets, and are ready to take prompt action if needed, hardened steel should be fine (it’s what I used).

Check that all magnets are in good condition, free of chips, to ensure maximum potency.

Consistency of Magnet Strength

Magnet strength (and size) varies drastically by manufacturer. Using neodymium magnets from Maker’s Supply is critical since this model is calibrated to them. If they switch suppliers in the future, results could change. In any case, these are inexpensive parts. Just add them to your next filament order to save on shipping!

If you decide to use other magnet suppliers and are ok tinkering with calibration yourself, note that size also varies significantly among brands. For example, the Maker’s Supply “4×2” magnets are just under 2 mm thick, but the cheap generics I had were about 1.65 mm thick. I expect some magnets could exceed the thickness of the Maker’s Supply ones, and if they protrude above your printed surface, they could damage your nozzle.

Safety Warnings

Neodymium magnets are not toys.

• Keep them away from pets and young children. Swallowing two magnets can clamp them together inside the digestive tract, leading to severe injury or death if not surgically removed.
• The 25×3 mm magnets are relatively strong. Keep away from pacemakers, and avoid handling them near other magnets or ferrous metals. If they freely collide, they can break or cause finger injuries, and shards can fly off and injure your eyes. They typically ship with spacers which will need to be carefully removed. A good technique is to stack them one at a time, carefully sliding the next magnet onto the stack from the side and then releasing once it begins to slide into place.

How to Print

Filaments

While I expect most any PLA will work, to improve stability (and to look cool) I used shimmer PLA (Bambu Galaxy & Panchroma Starlight) which are about 5% less dense than regular PLA.

Build Plate

I suggest a textured PEI plate so that the fragile parts can be easily removed once cool. Smooth plates might be okay, but avoid the super tack style of plate.

Base

All of my print profiles include both bases. Just print the one you want. You’ll insert magnets afterward (see “How to Assemble”), and they’re not secured in place so that you can adjust as needed.

IMO, base option 1 looks best, especially how its triangular pattern contrasts with the diamond’s. Note that it has a small window through which you can see the magnetic stack. I consider it a happy little accident in the design which looks pretty cool. If you prefer to remove it, you’re going to want to enlarge both the base and the diamond so they have consistent dimensions with each other, though that will reduce stability.

The top half of base option 2 looks good as a standalone base. It can’t hold as many magnets that way, however, so stability will be reduced in that configuration.

Sierpiński Diamond

There are 2 versions:

1. Pure diamond: This version shows its magnets and continues the fractal pattern all the way down. It is printed in 2 parts. Since it weighs ~1.5g less than the math-tipped version, it is more forgiving and more likely to stand straight.
    

2. Math-tipped diamond: This version hides its magnets and depicts the mathematical limit to calculate the diamond’s volume (assuming it was a pure fractal). It is printed in 3 main parts + a small filler square. It is at the very limit of balance, so printing it with heavier filaments than what I used, or even with very slight differences in magnetic strength, may cause it to stand at a slight angle.
   
   Update 2/9/25: To improve balance, I reduced the mass of the math tip by ~0.4 grams. If you've previously downloaded one of the math tip profiles, you can do the same by setting this object's “bottom shell layers” to 2 and “sparse infill density” to 0.

   

   
   Besides the filler square, you’ll also notice a “wipe + cooling tower” cube on the plate. This cube slows the layer speed as the print nears completion, resulting in a pointier tip.
   
   It also acts as a makeshift prime tower. Bambu Studio only adds its own prime tower for multi-color prints, to re-prime the nozzle after each filament swap. While this model doesn’t have filament swaps, it does include two pauses for magnet insertion which unprime the nozzle as a side effect. Rather than mar the main model with stray blobs, the unprimed nozzle will deposit any extra gunk onto this disposable cube instead. If you change any objects on this plate, verify in the Preview tab that this cube is the first thing printed at each layer so that it can serve this function.
   
   Unfortunately, I couldn’t use this technique for the pointy fractal objects due to the inherent limitations of spiral vase mode—however, any minor imperfections are far less noticeable on those pieces thanks to their triangular holes.

For both options, all fractal parts are printed in vase mode to minimize weight. For the magnetic parts, there are two pauses for when to insert the magnets. This is all already configured in my print profile.

First pause:

1. With your fingers, insert the 10x4x3 mm ring-shaped magnet into the slot. The N side of the magnet should face up, so check that the S side of the insertion tool sticks to the top surface of the ring. It should not, however, stick to the center part of the ring (which has inverse polarity).
   1. If you’re printing the math-tipped version, the ring magnet will be snug, so no glue is required.

   2. 

      The pure diamond version is looser, so secure the magnet with a couple drops of glue (especially important if you have a hardened steel nozzle which attracts magnets).

2. Verify proper orientation (polarity) by confirming that the N side of the insertion tool is repelled by the ring until you bring it close to the hole, at which point it should be attracted.
3. Push the ring down as far as it will go and verify that it doesn’t protrude above the print surface, to avoid damaging your nozzle. Resume printing.

Second pause:

1. Insert a stack of four 4×2 mm magnets into the center hole. The stack’s S side should face up, so use the N side of the insertion tool to insert it. You should feel the stack being repelled by the ring magnet as it approaches, but when it gets close to the center hole you should feel it being pulled in.
2. Push the stack down as far as it will go and verify that it doesn’t protrude above the print surface, to avoid damaging your nozzle. Resume printing.

How to Assemble & Display

1. Glue all parts of the diamond together.
   • Use glue sparingly – you can always add more. Don’t apply too close to the edges to avoid it oozing out.

   • 

     If you printed the math-tipped diamond, first glue the filler square to the smaller of the fractal pieces. This square fills a small gap which is an artifact of spiral vase mode. Once this filler is secured, wait a few minutes and then glue the tip to it.

   • For both versions of the diamond, glue together the top and bottom halves. Make sure to carefully align these halves before the glue dries. Use your fingers to simultaneously push in from all 4 sides at the seam, while also gently pushing the halves together.
2. Stack ten 25×3 mm magnets, removing manufacturer’s spacers carefully. Refer to “Safety Warnings” above for important handling tips. You probably won’t notice a difference if you use 8 or 9 magnets, but they come in packs of 10 so you might as well use them all. If you’re going to only use the top half of the base, just stack 5, but the diamond won’t stand perfectly upright that way (though it might be powerful enough to balance a pyramid).
3. Pack the base. Remove any supports from inside the base (only base option 2 has supports). Then insert the magnet stack with the N side facing up into the upper half of the base (the half which has a divot). Then, attach the lower half of the base.
4. Balance The Limit of Possibility by resting its tip in the small divot atop the base. If it is pulled down too strongly, you probably inserted the 25×3 mm magnet stack upside down. Flip it and try again.

Thank You!

Oh, and stay tuned for my next big illusion. Not being a performer myself, I've put my cringey demonstration video aside - I'm now working with a professional magician with 4+ decades of experience to do it justice. I guarantee it will be worth the wait!