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Question: Do you believe that a Level 4 Menger Sponge constructed entirely of business cards possible?
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 Author Topic: Building a Level 4 Menger Sponge approximation entirely of 2 X 3 business cards.  (Read 626 times)
Gleb Gamow
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 December 31, 2015, 01:02:19 AM

A video ref: Mega Menger: Building a Menger Sponge at MIT
Wiki: https://en.wikipedia.org/wiki/Menger_sponge

http://www.megamenger.com/

Quote
Current Level 4 progress: 100%

Our Level 4 Menger Sponge is made from 17 Level 3 sponges (pictured above), 5 partially completed Level 3s, 23 Level 2 sponges and assorted other Level 1 sponges in locations around the world.

As you read, a completed Level 4 Menger Sponge WAS NOT constructed. In fact, not even the task of building 20 individual Level 3s around the world was achieved.

The larger Menger Sponge pictured is a Level 3 made of 20 Level 2 Menger Sponges, in turn made up of 20 Level 1s, 400 Level 1 Menger Sponges total (8,000 individual cubes).

A Level 4 would consist of over a million business cards and measure 13.5 feet cube.

http://theiff.org/oexhibits/menger01.html

Quote
In 1995, Dr Jeannine Mosely set out to construct a level three Menger Sponge from business cards. After 9 years of effort involving hundreds of folders all over America, the Business Card Sponge was completed. In August/September 2006 the Institute For Figuring curated an exhibition of the Business Card Sponge at Machine Project [Link] in Los Angeles.

Dr. Jeannine Mosely is one of the pioneers in the emerging field of computational origami, a branch of mathematics that explores the formal properties and potentialities of folded paper. An expert on the subfields of business card origami and minimalist origami (in which the practitioner is limited to only four folds), she also conducts research on curved crease origami, investigating the forms that can result from non-linear foldings. Dr Moseley was trained as an electrical engineer at MIT and works in the computer graphics industry writing three-dimensional modeling software.

http://theiff.org/oexhibits/menger02.html

Quote
A level 4 sponge would require almost a million cards and weigh over a ton. I do not believe it could support its own weight - so a level 3 is the biggest sponge we can hope to build.

Do you believe as I contend that a physically completed Level 4 Menger Sponge constructed entirely of business cards is possible given the following restrictions? (see poll, with ability to change your vote):

• Quasi-standard American [paper] business cards (2 X 3) is the ONLY building material.
• All individual cubes measure 2" on all sides.
• No cutting or tearing of business cards.
• ONLY folding of business cards is allowed.
• No adhesives.

I'm confident that I solved how the structure would carry its own weight, but I'm a tad shy of being 100% sure that the four top center Level 3 Menger Sponges would stay in place even with what I've mentally devised as a unique solution. That's where any engineers reading this thread come into play: validating my approach which I'll present in the currently reserved second post of this thread.

I feel that monetary considerations is not much of a concern especially if a noble cause and reason is attached to the endeavor. Moreover, a permanent location for the structure for people to come and visit it is paramount oppose to building it, then tearing it down. Perhaps housed in a Menger Sponge-esque building adjacent to a freestanding Level 5 Menger Sponge constructed of 3,200,000 2" X 3" cubes (not of paper unless it's compressed waste products).

I'm almost sure the finished structure would be included in the Guinness World Records, albeit I don't know as to what category it would be under.
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Gleb Gamow
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 December 31, 2015, 01:02:36 AM

<This post is a work in progress, with this aside removed once finished penning.>

This post will depict my approach for the Level 4 Menger Sponge construction broken up in two parts: Ability for the bottom cubes to support the overall construction that I'm confident I've solved; The ability for the top four center Level 3 Menger Sponge structures to remain in place sans any outside forces.

The ability for the bottom cubes to support the weight of cubes above it:

I propose that the bottom cubes (not necessarily all of them) have inside of them the least amount of business cards rolled into cylinders standing on end. Just enough cylinders to achieve the task at hand so to add the least amount of weight to the overall structure. I constructed one such cube in like matter and it held up tens pounds for days without showing any sign of collapse, hence my confidence.

Proof of concept, as if I had to depict such to you braniacs. (got your attention yet?)

I believe it's very important that the creased folds be as crisp and uniform as possible, thus a machine should perform all the half inch folds at the ends of the business cards, not done by hand.

Part two, with a brief introduction:

I've constructed a Level 1 Menger Sponge in 2009   (okay, maybe it was more recently, but that shouldn't matter, right, Marshall Long and Leroy Fodor?)

I went to the local printer here in Sandwich, IL, to purchase his obsolete sheets of color business card stock which he cut into standard 2X3 business cards. After paying for them, I notice that some stock was thicker than others, but still paper oppose to being thin cardboard (cardboard of any thickness is not part of what I envision using). During our conversation after he asked what I was goin' to be using this for, the printer relaid to me how paper has a grain, and that's when it struck me on how to use that truism to construct a Level 4 Menger Sponge. It all boils down to carefully placing the folded cards according to direction of the grain of the paper producing a much stronger build. That, and employing various weights of paper within a certain weight parameter that's predominantly uses for business cards.

The only other difference in the cards is if the paper was specially designed, purposely making it stronger for the six(?) different weights needed for the construct. Now, I'm not talking about metal strands woven inside the paper, or any other substance that would be considered cheating, but a special paper formulated may be need for the structure to hold. Then again, not necessarily, but an option on the table nonetheless.

That said, there's one more trick I have up my sleeve as to how those top four center Level 3 Menger Sponges can be held in place.

First, let's recap:

Business card stock comes in different weights which would be used to our advantage: Heavier stock used on the bottom; lighter stock for the construction of cubes at the top. The placement of each card being crucial. Same true as to the weight of the stock used for the cylinders.

Paper has grain, another fact we can use to our advantage. If a business card is standing on edge lengthwise, it would hold more weight if it consist of two-inch vertical grains oppose to three-inch horizontal grains. More so being true if the card is laying flat, especially when used for the construction of the four center Level 3 cubes at the top. The grain must be taken into consideration for the construction of the cylinders to help minimize the number of cards needed for the build.

Now, for the trick I have up my sleeve which adds more weight, but hopefully it's desired affect offsets that while making those four crucial top cubes stronger and maintains its rigidness.

One more thing before I get into that. Temperature and humidity should be highly consider during and after the build since we're talking about paper. One can easily imagine what would happen to even the best paper structure built if the humidity were too high over a period of time. Perhaps, keeping the temp at a constant 70o would help maintain its integrity, always being mindful of body heat let off from those visiting the structure unless it's fully enclosed.

Actually, there's two tricks I've devised to hold the top four center sponges rigid. One, is to incorporate double flaps on the leading edge of each cube at both ends of the Level 3 sponge that's attached to the columns. The other is sliding an unfolded card on each side of the cubes that, again, are at the leading edge, all the while being mindful of the cards' grain direction. It's this aspect that needs scrutinized since Level 3 sponges weigh ~150 lbs each, thus 512 connection points will be holding ~75 lbs between them.

The decorative cladding would be of cards of lighter weight unless placed strategically for structure integrity. Same true for the makeup of cubes not having cubes directly above them.

The cladding cards could depict an image of a major sponsor, or once finished all the cladding combined depicts a large image representing some sponsor.
Gleb Gamow
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 December 31, 2015, 01:05:52 AM

I have procured a marketable .com domain name consisting of only five letters that reflects the challenge. I was surprised that it was available.
Spoetnik
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FUD Philanthropist™

 December 31, 2015, 02:44:05 AM

Ya eh ?
I had to Wikipedia it LOL

Bruno.. you sooo crazy

FUD first & ask questions later™
Gleb Gamow
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 December 31, 2015, 02:57:02 AM

Ya eh ?
I had to Wikipedia it LOL

Bruno.. you sooo crazy

Yeah, but in a good way.   Anyway, do you think it's possible? And, I hope it wasn't you who voted yes (two votes to date, one is mine) so that you can get you balls cupped.
Spoetnik
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FUD Philanthropist™

 December 31, 2015, 06:02:29 AM

I dd not vote.

I am still trying to figure out what a fucking "Gleb Gamow" is ROFL
Anagram of some kind ?

FUD first & ask questions later™
Gleb Gamow
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 December 31, 2015, 06:30:54 AM

I dd not vote.

I am still trying to figure out what a fucking "Gleb Gamow" is ROFL
Anagram of some kind ?

My birthday is March 4. Search this section of this Wiki page for Gleb, then Gamow for your answer: https://en.wikipedia.org/wiki/March_4#Births

BTW, what's a Nag A Ram?
Spoetnik
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FUD Philanthropist™

 December 31, 2015, 06:37:56 AM

Ok so i can quit thinking i might figure it out one day LOL
I am not the guy you need for this topic hahhaha
Maybe someone smart will come along and reply

FUD first & ask questions later™
serenapj
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 January 01, 2018, 07:46:20 PM

I have construct a 4-level origami Menger sponge but I used a different technique based on strips of paper. The business card method is not good for a level 4. It will collaps for the weight. My method is too much solid so it had be possible to made it.

https://www.facebook.com/menger4/
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