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IamZandar — Hilbert Cube In Blender
Published: 2015-01-26 01:39:43 +0000 UTC; Views: 2127; Favourites: 17; Downloads: 13
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Description
An example of a model not possible to create without complex formule. This is the Hilbert curve made with a Python function from C code. This is a model of impossible complexity on the inside, and not to be made by hand. At least not to my ability. So I turn to the power of Python, and math formule for answer in Blender. There is many thousands of polygons, but Blender still did not fail! Render with Cycles.Related content
Comments: 31
Nice !
Did you even try placing the camera inside ?
And giving it a glossy material ?
This could give interesting perspectives and surprising effects !
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I will have to try. There is not room inside for camera. The cube is full of the maze shapes.
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Oui, the Star Trek no? I was thinking about that too.
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They also use Hilbert curve for rendering bucket path in many render engine...
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Oui, a 2D Hilbert path. Very interesting.
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Oui, it is. I think it not a model to make otherwise by the hand. I am not the best at hand models, but this would be to challenge even the best I am certain.
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I probably could do it by hand, but the question is, do I want to?
Each side looks to be unique, judging by two sides alone. There are 40 courses vertically and horizontally, meaning there are 64,000 courses throughout. It's not like a Celtic knot (without an end) as there are 27 beginning/ending points on the front face alone. If that same number holds true for each face, then there are 81 complete entities running throughout and I'll estimate that each entity touches each layer of each course 790 times.
Alternatively, if there were 27 beginnings/endings on each layer of each course and each face, then there could be 1,728,000 complete entities, and each entity would only touch 27 layers.
(I'm sure there are other possible alternatives, I just mentioned the two that sprang to mind that had simple rudimentary patterns to allow an estimate of parameters.)
In either scenario, a lot of backbreaking work, and while I like a backbreaking challenge, there wouldn't be any satisfaction beyond completion of a challenge. That's usually not enough to keep me going.
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How you did it, it would take me about a year and a half to replicate it, depending on the two alternatives I described. If it is one entity, I might have it done in two to three days, because it is much easier.
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...as there are 27 beginning/ending points on the front face alone
I'm not sure what make this model looks like the image above, but theoretically this Hilbert cube is supposed to made by one single entity. Hilbert curve fills space with itself.
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I had to look up a Hilbert cube last night myself as I wasn't familiar with what one is, but there was nothing that seemed to say it had to be a single entity, but there were two words that suggested that this isn't a true Hilbert cube, and that was "infinitely countable" suggesting that a Hilbert cube is a theoretical manifestation alone, much like a tesseract. There is no way to physically manifest a theoretical entity without setting some limiting parameters.
OR, the person that lent IamZander the equation, did so in a way so that their work (a single entity) would remain unique while IamZander's would be a close approximation.
Either way, this still is an impressive construct of a theoretical entity.
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I think it had to be a single one and only one. Otherwise it's not Hilbert curve (as I the way understand the name of this deviantion, the cube in this render make by a single "spline" object that follow Hilbert curve (fill 3d space in this case. More familiar, In rendering bucket order, they use it as one of bucket trajectory options, which to fill a 2D image in rendering process). Maybe the guy render this one didn't mean that)... if it couldn't be that then we should call it another name.
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Perhaps you are right. I just looked it up again and I saw that it said it's a continuous fractal.
Should an artist who is trying to replicate the Mona Lisa, call it something else because it isn't a perfect rendition? Hrm. I'm going to stand firm against you on that call. If he initially decided to call it something else, then people would probably stop by and say "Isn't that an attempt at a Hilbert curve?"
In other words; you can't please all the people, all the time.
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Making it a single entity would make it much more simpler to do by hand, not harder.
So, you are being adversarial by attempting to impress by affecting greater importance in knowing exactly what a hypothetical physical impossibility is, opposed to my boldness in knowing how to do in long form, what this artist did in short?
In other words, you are fighting my arrogance with your own pretentiousness?
Yeah, I'm done with this conversation too but don't worry, I'm not small minded enough to do something churlish like block you because you don't agree with what I think.
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I stand against you and your statement, not him 
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I will check with the author of script for distribution. It is not my code, and was kindly shared to me. The original was created on a CVS spreadsheet. You will need still another script to convert the CVS information to Python to use in Blender. You can find that script here:
blenderartists.org/forum/showt…
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Passes the baby bottle.
...you said you wanted the formula.
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Catches it ands it back.
Its for you.
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Heeeeey! I don't need the formula!! ...is it still warm at least?
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