Archive for the “Special Projects” Category

The cup with the funny bit in the middle is a Pythagorean Cup – 3D printed – 13 hours and 160 gramme of filament.

A Pythagorean Cup is a weird beasty – it prevents piggy drinkers.  If you fill up the cup to below the line on the rim (below the top of the domed piece in the middle) then you can drink from the cup, no problem.  If you fill the cup to above the line, then a siphon (which is within the domed piece in the middle) will empty the cup through a hole in the base all over your lap.

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The 3D printer has been working overtime recently turning out fractals.  Here we have Sierpinski (triangles) and Menger (square) sponges.

These objects are 4″ on a side, the Menger Sponge is 4th order and the Sierpinski Sponge is 6th order!!  Both are 0.2mm resolution printed using white Rigid.Ink PLA and a 0.4mm nozzle.

The Sierpinski Sponge was a modest 30-hour print and the Menger Sponge was a humungous 65 and a half hour print.

I am thinking about printing a 5th order Menger Sponge, again around 4″ on a side – but this will take around 90-hours in total.

May also print a larger Sierpinski Sponge at higher resolution (0.1mm).

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Another marathon mathematical object run for the 3D printer – this time the Roman Surface (seen here in front of a Klein Bottle).

I had generated this surface years ago using Mathematica and had spun the object around in 3D, but still couldn’t quite assemble the thing in my head.  Now I can hold it in my hand I can see it clearly.

The 3D printer has been taking such a hammering with these extremely long prints that the X Y bearings are now sounding a bit klunky.  New bearings are on order.

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After printing out the Sierpinski Triangle I thought I would go for a LOOOONG print.

So I went for a Klein Bottle (see Cliff Stoll’s You Tube presentations on the Klein Bottle – they are excellent) and a BIG one.  The Klein Bottle I printed out ended up 8″ tall and 4″ across the base.  This was printed at 0.2mm resolution and the print time was 18 hours!

Clearly it was a mistake not to use transparent filament for this object (or indeed for ANY 3D mathematical object) but that has been rectified by me ordering “natural” and trans-blue filament from Rigid.Ink.

In the meantime I thought it might be interesting to illuminate the Klein Bottle to see if it revealed the internal structure.  It didn’t – BUT – it did show up very nicely the printer’s print pattern in the wall of the bottle.  This is in fact the strengthening framework that lies between the inner and outer walls of the bottle (the walls are not solid).

The clear filament arrives on Monday – I will then need to give this one another shot.

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I bought and recently assembled an Anet A6 3D printer.  Highly impressed by what you get for the money.  Been running calibration prints and test runs for a couple of days before doing my first serious 3D print.

I bought this printer with one aim only – to print out 3D mathematical objects.  I have printed out a couple of very small Menger sponges, and then I printed out this larger (3″ on a side) Sierpinski sponge.  Took around 9 hours to print this out at 0.1mm resolution.  It looks way better to the eye than it does to the camera.  I took the picture with it still attached to the Anet A6 bed as I might well destroy the thing in trying to get it off (it sticks rather well to the BuildTak).

Next print will either be a Klein bottle or a large (4″ on a side) Menger sponge.

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See a You Tube video of last night’s 10 p.m. ISS pass here.

Mute the audio when playing.

The ISS will make an appearance about a minute in towards the centre/right.

The ISS exits top-left.

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If you had clear skies last night you may have noticed that Jupiter was very close to a 12-day old Moon.

The main image is a fisheye lens view of the scene over the New Forest Observatories, and the inset top-left is a telescope view of the encounter.

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So the Prime Number the MegaNode computing facility just found has now been confirmed – it is:


Which is 388,342 digits long and is in the top 5,000 largest primes.

I just ran the numbers through Mathematica to see what the whole thing looks like – it takes up many pages – and the last digit is a 9.

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As we are entering galaxy season, Leo is well-placed for imaging.  So I went for a deep shot of Regulus as I wanted to get the dwarf galaxy Leo I.  What I was not expecting to get was this object in the FOV – 

Thank you Jim at EPOD for continuing to publish my work.

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