Fractal Pyramid with Continuous Cross-section

by ricktu, published

Fractal Pyramid with Continuous Cross-section by ricktu Feb 20, 2016
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42674Views 12112Downloads Found in Math


No supports. No bridging. No retractions.
It has the astonishing property that the horizontal cross sections are simply connected and change continuously with height, so can be printed perfectly with spiral mode (or single-walled without infill).

cross section animation

This fractal is half of the octahedron flake (or Sierpinski octahedron). Every triangular face is a Sierpinski triangle, and the base of the pyramid is (approximately) a space-filling curve called the Sierpiński curve. Figures like the Vicsek fractal also exist in this model.

Print Settings

Printer Brand:



prusa i3


Doesn't Matter








Printed with the "spiralize the outer counter" option in Cura .

The original scale is to match the limit of a 0.4mm nozzle..

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I have made several of these. Your code is superb!! Thank you :)

Bravo!! This print is amazing and the GIF kept me entertained for hours, so satisfying. Thank you for uploading this amazing file. :)

I made the pyramyd4.
So surprised to discover this function in the Cura Slicer !
I never imagined my 3D printer would be able to make so tiny details.

Thanks for sharing

Maybe I missed it but what is the difference between pyramids 4-5-6?

May 18, 2017 - Modified May 18, 2017
Mythobeast - in reply to Jeeperforlife

The number is the fractile iteration of the Sierpinski solid. In plain English, a 5 is four 4's placed in a square, with a fifth 4 stacked on top of them.

A 6 is a repeat of the previous cycle, using 5's instead of 4's.

Note that each of these versions appears to be scaled down so that you get the same size, just more detail.

This is one of the coolest, if not the coolest print I have done. Plus it will find all of the loose fasteners in your printer very quickly. :)

Slic3r Prusa Edition slices these models quite quickly and accurately. Vase mode works well if the layer height is kept low (I ran it at 0.10)

For what it is worth, Slic3r will do this model, but it takes a LONG time. It seems to get stuck calculating infill (which is not needed since you are doing a spiral vase) and it takes a long time. For the 4 it is tolerable, for 5 it is painful, and for 6 it is a leave it overnight. But it does work.

Apr 18, 2017 - Modified Apr 18, 2017

Anyone else is having problems to slice this in Slic3r?
I've set the infill to 0%, disabled supports, set retraction to 0mm and enabled the spiral vase option. But Slic3r keeps adding infill lines.
Using the g-code viewer from octoprint I can verify that the infill code is indeed being added to the print.
This is happening with the pyramid5 version, the pyramid4 does fine.

Try reducing the layer height.
And try Slic3r Prusa Edition.

In order to get this to print without retraction in Simplify3D - uncheck "retraction" on the extruder tab, on the layer tab check "corkscrew/vase" mode and set top and bottom solid layers to 0, and on the advanced tab check "merge all outlines into a solid model". After doing this, it is printing beautifully using a single layer. So cool to watch this thing grow!

Thank you! I tried setting only "vase" mode on and it was a complete disaster...

You used no retraction?

Mine came out great
Had to print with a raft
Without it, all i got was a mess of pla sticking to the nozzle
Used 200c (pla)and a bed temp of 50C and it took about 2 days to print

this might sound like a stupid question but...
whats the difference with pyrimid4, and pyramid5

Did this and it came out great. Thx a lot for sharing.

Jan 6, 2017 - Modified Jan 6, 2017

This is one of my favourite prints a Sierpinski Fractal Square-Based Pyramid, created on a Flashforge Finder. I did a video and added the correct credits both in the description and video. https://www.youtube.com/watch?v=wPIWJXdHqwQ

It's probably the most retract intensive print I've ever come across.

It is designed to be printed without retraction at all.

Yeah not getting the no retracts thing either. Printing with spiralise and retracts and plentiful as are non print moves obviously.

You say no retractions but my printer is retracting like crazy. I used the Spiralize Outer Contour mode in cura with 50mm/s and 0.1 mm layer height. Does the layer height have to by 0.2 mm?

You say no retractions but my printer is retracting like crazy. I used the Spiralize Outer Contour mode in cura with 50mm/s and 0.1 mm layer height. Does the layer height have to by 0.2 mm?

I'm getting a lot of stringing with this model. Any general suggestions?

i cant seem to get vase mode to work properley in simplify 3d. the preveiw still shows alot of travel moves over gaps.

It seems not possible to achieve printing this model in one continuous line with S3D. At least no option I tried resulted in it. Always lots of travel moves in between.
With Cura it works flawless. Strange.

Had no luck with Cura :( Lots of travel moves! Can you share your settings?

I got good print without the spiral vase and I did not see this description and not and had problems with s3d now I got a picture of the result

Very, very cool model!
May I ask which software you used to design this?

I used 123D Design.

How long does it take to print? I'm printing at a place with a two hour time limit. By the way, it looks absolutely amazing! Thanks for uploading it. :)

pyramid6: 12hrs
pyramid5: 2hrs
pyramid4: 20mins

Pyramid 6 took me 11.5hrs at .2mm

I just printed pyramid 5 today and I can't tell you how much I love this model. it's so well done and perfect for 0.4mm nozzle. I just started a pyramid 6 and will let it run overnight to greet me in the AM with it's mind blowing beauty. I could look at this thing for hours, turning it over and over in my hands.

Could you tell me how you created the cross section animation GIF file?

I used 3D-Tool to view the cross-section of the 3d model, then recorded it with a screen recorder while holding the "change cross section position" button.

haha clever!