Sierpiński Pyramid (Customizable)

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Sierpiński Pyramid (Customizable)

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Print Profile(2)

All
A1 mini
P1S
P1P
X1
X1 Carbon
X1E
A1

With Base Layer
With Base Layer
Designer
17.7 h
4 plates
4.9(34)

No Base Layer
No Base Layer
Designer
17.4 h
4 plates

Boost
259
459
63
30
656
207
Released

Description

Intro

The Sierpiński Pyramid is a 3 dimensional manifestation of the Sierpiński triangle.
It's a fractal, that is subdivided recursively into smaller and smaller pyramids.
In (mathematical) theory it goes on and on into infinity, which means you would be able to zoom in infinitely and still see more little pyramids.
Unfortunately we live in the real world where there are no mathematically precise fractals. The next best thing we can do is to show a subset of the fractal.

Print Settings

The Pyramid is printed in Vase Mode. With that said, it's incredibly sturdy. I wouldn't be afraid to literally throw a level 6 pyramid around.

Versions

I've uploaded different recursion depths (or levels if you want to be one of the cool kids) which show off the beauty of the Sierpiński Pyramid.

For every level you go deeper, the longer it's going to take (like in inception) and the more filament it's going to use (not like in inception).
In the print profile you can find the levels 3 to 6, which go from 6.5 minutes to a whopping 14 hours. I recommend printing a lower level first to check if everything is alright with the printer (and you).

 

I've also uploaded the different levels with a base layer and without base layer. The one with base layer is more stable since it it can't bend at the bottom, it also helps with the first layer sticking. The one without base layer prints faster and uses less filament, although the difference is basically negligible. See Print Info below to compare.
The version with base layer also gives you the added bonus of creating a Sierpiński triangle when held up against the light.

Parametric adjustments

Maker World introduced the option to adjust parameters with OpenScad files. Unfortunately rendering a Sierpiński pyramid takes ages, and the model generator already gives up at level 5.


Parameters

level: the level of the pyramid
side_length: the side length of the unit pyramid, that is the smallest unit of pyramid in the fractal. By default it's 1.875 which causes a level 3 pyramid to have the side length of 15mm. The formula for calculating the side length is `{side_length} * 2^{level}` so if you were to choose a side length of 2.5mm, then level 4 would be `2.5 * 2^4 = 40mm`.
overlap: the overlap between unit pyramids. Setting this to 0 would create a perfect mathematical Sierpiński pyramid, however it would be impossible to print since nothing is connected and therefore everything would be floating. Setting this too high ends up making the fractal look less detailed.
base_height_ratio: this is the ratio of the base to the height (parallel to Z axis). By default it's the square root of 2 which causes the pyramid to be equilateral. Setting this to `pi/2` gives you the ratio of the pyramids of Giza (presumably)
base_offset: By default this is 0, which gives you a model with a base layer, the higher this is, the more of the bottom is cut away. The range of this variable is [-1:infinity (probably)]


Print Info

(On the A1 & according to Bambu Studio)
No Base

LevelTimeFilament
36m32s0.25g
427m37s1.32g
52h25m7.69g
614h00m45.88g

With Base

LevelTimeFilament
36m47s0.27g
428m27s1.39g
52h28m7.99g
614h18m47.42g
7 pls dont print this3d9h52m296.20g


Potential Problems

First layer not sticking

The biggest culprit for me is forgetting to wash the build plate from time to time.
If you experience the first layer not sticking you could try to:

  1. Wash your build plate
  2. Use a textured PEI plate
  3. Use glue
  4. Use the pyramid version with base layer
  5. Slow down the first (few) layer(s)
  6. dry your filament?
  7. use different filament?
  8. i'm just guessing at this point

Nozzle too close to build plate / Extruder gear slipping

For some reason this always happens to me when I use the 0.2mm nozzle, not sure if something is wrong with the nozzle, the printer, the slicer or with me.

You'll know it's too close, if the extruder can't push any filament out and the extruder gear will therefore slip. The slipping will make clicking sounds, so please watch out for that when printing the first layer.


Nevertheless, to combat this I change the Z-Offset in the slicer. Unfortunately there is no setting to change the offset, you'll have to change it in your printers start gcode. (Orca slicer has a setting btw)
Somewhere at the bottom of the start gcode you should find

;===== for Textured PEI Plate , lower the nozzle as the nozzle was touching topmost of the texture when homing ==
;curr_bed_type={curr_bed_type}
{if curr_bed_type=="Textured PEI Plate"}
G29.1 Z{-0.02} ; for Textured PEI Plate
{endif}


Remove the minus from `G29.1 Z{-0.02} ; for Textured PEI Plate` and choose `Textured PEI Plate` as your plate type
Little tangent: In case you were wondering, choosing `Textured PEI Plate` over `Smooth PEI Plate / High Temp Plate` just changes the Z offset as far as I know. The comment in the first line of the gcode snippet explains it pretty well.
Changing the offset from -0.02 to 0.02 essentially raises the nozzle by 0.04mm from where it usually would be. If the issue persists, just raise the offset by more.

If more people are having this issue, let me know in the comments and I'll upload a version with adjusted Z offset.

 

Filament stopped coming out of the nozzle

Most likely heat creep. Happened to me when trying to print a level 7 pyramid with matte PLA. To combat this you might want to try printing cooler than normal. To fix this you could pause the print (if the stopping just happened) and unclog the nozzle with an acupuncture needle. If the heat creep happened a while ago you could cancel the print, set the print bed to the printing temperature and unclog your nozzle. Once that's done you can do some Gcode trickery to resume from the failed location. That is all theory though, I have no idea how to do this unfortunately

 

It looks too cool

Not sure how to help you with this.
 

Where is Level 7?

While Level 7 fits on the 256mm build plate, sorry A1 mini :(, it takes 30minutes to render in OpenScad, way too long to slice in Bambu Studio and around 20gb of ram. I'll upload the 3mf for a level 7 in case you like suffering. 
 

Where is Level 8?

Ok don't get ridiculous

but just to do the math. Going from one level to the next basically multiplies the material by 6, so level 7 is ~300g which means level 8 is ~1.8kg. Time should also be factor 6, however in reality it seems a little less, so 3d10h print time at level 7 becomes ~20.5d at level 8. Since it's a little less than 6x, lets say ~20d give or take. You also need a print volume of 480mmx480mmx340mm, if you want to print it in one go, which would be one big chungus of a build plate if you ask me.

 

Closing Thoughts

If you print this, congratulations. You are now in possession of something special. I never get tired of staring at the fractal. But then again, I'm pretty weird.
There is something unique about holding a fractal in your hands. Also it's pretty weird to hold in your hands in general, since it weighs like nothing.

Also I'd love to see your prints with your amazing filament choices!

Comment & Rating (63)

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Cool looking model! I have a question: I downloaded both the print profiles and noticed some weird behavior with the slicing. It seems for every level model, there's a missing section on layer 2 -- all in the upper left quadrant. Pictured below is from the models with a base -- the models without a base also have the same missing section. Even when you view layers 1 through 3, you can see that there's a layer missing here. Are you seeing the same when you slice the model, or is it just me?
The designer has replied
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Hey, thanks for the comment! Yes I do see the same thing and was wondering about it as well. My theory is that happens due to slicing in vase mode, where the missing section is printed by the "layer" above. Since in vase mode there are no layers I've noticed often times sections missing since the slicer is confused about where to display those lines. But that's just a theory. A slicer theory. Anyway, I've printed so many of these that I can confidently say that if your printer is working as intended with a 0.2mm nozzle, the pyramid comes out beautifully :)
(Edited)
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Replying to @Raybesh :
I think you're right. v1.9.1 of Bambu Studio just dropped, and they mentioned they rewrote the Spiral vase mode! It fixed this missing section in the model, but now it's adding erroneous paths at higher layers. :( Here's a screenshot of the Level 5 tetrix at layer 49
(Edited)
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Replying to @gillithonnen :
Very interesting, I'll need to take a look at the changelog. For the print profile I used 1.8.4.51, which is where I see the missing sections you mentioned. Have you tried to print the pyramid with the gcode from 1.9.1? If yes how did it came out? I'll try out later and if it breaks I might need to open an issue on github.
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last hour on Level 7. I had printed a pyramid a few months ago when I found a version on printables, that was a level 6, so I knew I had to go that extra mile this time. longest print I've ever done, but I think it's worth it! printed in Transparent Purple PETG. can't wait to get a light under it for display!
(Edited)
The designer has replied
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Holy crap you actually did it! Mad props on having the courage to do it. Did you take any precautions on heat creep or other types of failure? Heat creep is what got me last time when attempting this. Now that someone is actually in possession of one of these I'll have to render level 8, so see you in about year when it finishes rendering 😂 you could technically print 5 more of the level 7s and glue them together to create a level 8. I mean it wouldn't fit on the 256mm³ build plate either way :( So happy you did this and actually succeeded, you are now morally obligated to bless the world with pretty pictures :D
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Also: what the hell is going on with the hole on the side of your print head? 😂
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Replying to @Raybesh :
I'll put the date in my calander😂 could you imagine it rendering to say 80 or even 90% and you get a black out...😑 I Honestly don't even know if the processing power would be able to handle the full level 8. This one more so than the level 6 I printed previously provided some unique hurdles. Both trashed SD cards. This one actually ate through two SD cards & failed twice before it went right. But I had sort of expected it to as the level 6 had done similar to me. It's like the first time you go to print it, or at least for me on both level 6 & 7 the print will start get no more than an hour through & then cancel itsself. I like to think its the printer just saying "Nope. You're Crazy. I'm not doing it." after that failure the sd card was unreadable. Put in a brand new SD Card, it got an hour in (Finished the base layer only) & was Done with it again😂 but just like they say "third times the charm." Put it on turned off the timelapse (to help prevent the SD Card Imploding) &I knew once it had made it through the first level it was good. HAHAHAHA! Don't Tempt ME! I honestly would. I could watch this print start to finish & still be fascinated.. It's just one of those things That is actually the secret to the confidence!😅 As I used to get constant heat creep with both PLA & PETG (Mostly with the door & lid closed & on respectively for the PETG). Anyway I'd tried a bunch of different things with little to no success & it was starting to get to me, Then I watched some random You-tube video (Dont remember how it came about) , anyway the guy had done the same (Albeit less axe murder through a door looking) alteration for his tool head after experiencing almost the same issues Given I was pretty much ready to beat my own head against a wall I figured what do I have to lose, as I can always order a new face if it somehow makes things worse or doesn't help. But. I kid you not, since I made that minor renovation I have not experienced heat creep again (Except one time I accidentally closed it all up on a hot day printing PETG, but that was user error not a machine issue🤪😂) you wouldn't think removing the perforated area entirely would have a huge effect but I swear by it. I'll post some more photos shortly. Still trying to find the best way to display it. & thanks again for the model! truly an awesome thing to behold.
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Print Profile
With Base Layer
fractalicious print!
The designer has replied
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Gorgeous! I see you chose level 5, it's in my opinion the sweetspot of something pretty while not going full haywire with a 14h print 😂
(Edited)
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Print Profile
With Base Layer
turned out great. Love this model
The designer has replied
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beautiful choice of filament, thanks for sharing! :)
(Edited)
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Boosted
Print Profile
With Base Layer
awesome print! after a few failed prints due to bad dual colour silk PLA I tried standard PLA and it printed flawlessly. it blows my mind that these printers can print an intricate model for 13+ hours without even a single issue. photos are of level 6 in Bambu PLA basic bronze
The designer has replied
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I'm so happy it worked out for you! so the issue was silk pla after all? I'm not sure what is in silk pla but it's bed adhesion is off the charts And I agree, the precision and endurance of these printers is insane Congrats on the good looking level 6!
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Print Profile
With Base Layer
Printing this with a tri-color silk PLA filament is amazing, although slightly more hassle getting the silk PLA to behave compared to PLA basic (printed in blue).
The designer has replied
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Beautiful! What happened to the failed print in the background if I may ask? Something I could have improved on my end?
(Edited)
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Replying to @Raybesh :
That failed because the nozzle clogged l, nothing you can do about that 😅
(Edited)
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this was my favorite print to date. you really shared something special here, thank you! I wish it were possible to print level 7 without the massive time jump, but level 6 is as cool as I’d hoped. great design!
The designer has replied
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Thank you so much! I really appreciate it :) I agree, I'd love to have a level 7 as well but the commitment and fear of nozzle clog is real 🥲 you could technically print 6 level 6's and glue them together to make a poor man's level 7, but that would take in total even longer than printing level 7 at once. The benefit would be breaking it up into smaller prints and therefore not occupying the printer for 3.5 days Love your choice of filament! The fade is gorgeous 😍
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Boosted
Any tips for removing from the plate? My first layer was perfect, maybe a little too perfect as even after an hour of cooling it wouldn't come loose from the textured PEI plate. I flexed the plate gently and that caused the top part of the pyramid to come loose leaving the bottom row of pyramids still firmly fixed to the bed. I think this silk PLA does have issues with sticking firmly to the bed and also issues with adhesion between layers so it's not a fault of the model, but interested in how others have removed it in one piece.
The designer has replied
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Hey there, thanks for the comment! In the description under Potential Problems I wrote a section about the nozzle being to close to the build plate. That causes the extruder gear to slip and make clicking sounds. Did you happen to observe the first layer being printed? Besides that my bambu silk pla also sticks way too aggressively to the build plate. I still have filament stuck to the textured plate from a calibration I did a few days ago 🤦🏻‍♀️. Good thing you only printed a level 4. If you went for level 6, that would be way sadder :( Anyway please do try normal PLA and observe the first layer and check if the extruder gear slips! Best of luck :)
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Stunning. No problems while printing. Level 7 is tempting!
The designer has replied
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Yeah I feel that, but a 3.5 day print with a 0.2 nozzle has a high likelihood of heat creep or other forms of nozzle clog :( If you attempt it, and manage to print it successfully, please let me know what filament you chose and with what settings!
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Print Profile
With Base Layer
awesome nice work! did mine in metallic green purple :)
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