Here is a property I think real life fractals would have: at very small scales, the valleys of the fractal approximate the wavelength of light, so on a macroscale some fractals could display structural coloration (like in butterfly wings)
You could demonstrate this using longer wavelength radiation comparable with the size of the smallest detail; this would have to be microwaves or millimetre waves. At the moment I don't think there's any 3D printing technology which has the half-a-micron resolution you would need to get the effect with visible light.
This is such a fascinating idea, coming up with several fractal surfaces and computing the interference and scattering effects involved. Each fractal would likely get its own color and interference patterns. Lovely.
As a vfx artist, I love it when people outside the industry run into the issues we deal with on the daily. The perspective discussion in the beginning is something I have very often with directors and cinematographers, even the most seasoned professionals have a hard time understanding why you can't just slap two pieces of footage together without taking all of that into account. To get this perfect you probably need to take lens distortion into account as well, as the edges of the frame can be slightly stretched compared to the center of the image, so when lining up the whole of the image with a different perspective distance, you're can be a fair percentage off from distortion alone because of a largely imperceptible bend. A rectilinear lens can reduce this effect for all intents and purposes, if it's a good one. The final piece to this puzzle would be to motorize the focus so you don't get that artifact as well, and this could also be shot stop-motion style for a perfectly stable and crisp look. And for the record, I don't think this looks like CG necessarily, you probably could recreate this look in CG, it's just that you wouldn't get this without having this particular photographic reference as a starting point, so it's plausible as CG, but not clearly CG, even the smallest imperfection takes work which is the inverse of what happens in real life photography, so it's actually pretty hard to create a photo that definitely looks CG, it has to be extremely exact, it's an artform in itself.
The issue of lens distortion is something I’ve been leaving in its can (with all the other worms) and trying to not think about! You’re right that it doesn’t look that much like CG, which is probably for the best. I’ve run into the issue more with stills, like my current avatar photo (illustrating stereographic projection). With video, there are so many more things to notice.
It seems like the loss of focus is being used to help hide the loop, which is clever, though it would be really cool to see one that stays in focus too! Phenomenal video
I’m pretty sure that the blur is only there to prove that it’s not computer generated, as he mentioned he left mistakes in for that reason. I also wish that it didn’t go out of focus because then I’m pretty sure it would be perfect
@@christophermoore6110I was half joking about the mistakes. I’m still far enough from perfection on these loops that there is plenty of room for improvement.
The blur for me was what kept telling me it was a loop :/ I'd rather see the imperfections as you get closer in high fidelity and transition to the farther image than rely on blur if it was one of the "intentional mistakes" (which I doubt). Even with the out of focus shot you could start the transition between loops earlier to hide the blur, but then you lose more of the sharp frames and also the video would become mostly edited instead of mostly real footage @@henryseg idk if you can motorise the focus or if autofocus is accurate enough to go the right way without overshoot, or if focussing on infinity is possible. I wouldve suggested using a "camera" that can capture orthographically (therefore you can forego the whole rail setup entirely and zoom digitally) but the perspective..uh perspective..is a really cool way to convey the shape
I suspect that the camera may get closer to the fractal than its lens' minimum focus distance, which causes the blur. Or perhaps it's set to manual focus and that's why it gets blurry. It might have been interesting to see a camera with a longer telephoto lens set further back from the fractal and turn on auto focus with the center of the sensor as the focal point.
Amazing work! It really does look like CGI. I wonder how close you could get a natural fractal to behave like this, like with a fern leaf or broccoli. Less precise than a 3D print I assume, but the detail is better than the print resolution, so it wouldn't look as blurry.
the blur isnt from the object being 3D printed, its from the camera moving closer but still having the same focal length so the object starts to get blurry. If he could also change the camera focus as it slid forward he could make it look much better, and then the 'revert to start' part wouldnt be as obvious as it is now
@@SpydersByte It's both, you can see that the 3d print only gets so detailed. If there was no blur the lack of fine detail when zoomed in would be more obvious.
This should become a videography hobby in and of itself. The end product really is stellar and you did a good job overcoming the challenges that can arise from this kind of work that requires precision and accuracy. 😁
It is neat how doing it in real life rather than with post processing in software from a photo removes that weird uncanny artifact of smudging. The two products next to each other would not even have a contest because this is in a league of its own.
The fact that the linear speed has to be exponential while the rotation speed has to be constant, is another clever reminder of the complex relationship between sinusoids and exponentials.
@@adi-ow1cg You should look up Euler's identity. It shows how if you think of x as being some angle in radians then e^(ix)=cos(x)+isin(x). The relation is probably much deeper than this but i think this is what they are referring to.
Rotation speed doesn't have to be constant. The camera motion is in a completely different axis to the rotation speed, so no wonder rotation speed is irrelevant. But the orientation at the end of the loop must match as it was in the starting if the images are to line up. That can be achieved even with chaotic rotation.
@@adiadiadi333 Sure, there's no constraint on the absolute speeds of either component, but the relationship between rotational and linear speeds definitely is constrained.
1:46 this is the first video i've ever seen that understands that yes, 2d worlds have parallax!! you don't need to have a fog or have objects glow to discern depth in 2 dimensions, you can judge distance by the width of things alone- THANK YOU
I was really excited for this because I recently printed a fractal of the Sierpinski triangle and it's one of my favorite prints. Printing fractals is one of my favorite uses of 3D printing as a beginner.
You could potentially coat the model to reduce the subsurface scattering that is occurring after zooming in. Also, a point source light could reduce the scale variance in the lighting.
The continous loss of focus unsettles me on some deep level. Gets my skin crawling to a point where I just want the perpetual loop to end as soon as possible.
i like the transition between blur and clear focus. it also adds to the computer-generated look by making it look like the next fractal iterations are loading in
This is incredible. Sometimes what can seem like a really basic shot to a complete amateur (like me), can teach you so much about how it was made, and why there’s nothing basic about any part of this shot. There’s so many cool things about this print, and so many problems in creating this, that I would never have appreciated if I just saw the loop alone. It’s analogous to a fractal itself. The more you look, the more you see. It just goes deeper and deeper and deeper.
There are many videos i have watched on youtube, but this is quality. I can tell I"ll be coming back to rewatch this ,thanks for detailing your process, legend!
What a madman! It's unfathomable the size of his brain just to get the animation recorded and edited, but to explain the process and all the related concepts? My god
Fascinating work! If you have a camera with manual focus adjustment you can get a perfect focus for the whole movement like how the movies use a person doing it manually called focus puller.
dude. youre a genius Ive tried to do a simple animation loop in my comic "hole" and cant do it properly and its just a 2D drawing!! youve dome it with a 3D PHYSICAL OBJECT!! its amazing!
The way the structure is, it really seems like you could play with many ways of lighting the piece up. To highlight & contrast the textures of the design.
While moving the camera is the only way to perfectly replicate the dimensions of the fractal, it would probably be close enough to use a long focal length (the longer the better) and then do a digital zoom. Once your focal length gets long enough you may as well have an orthographic camera, and this technique has been used for some other real life illusions that require an orthographic perspective.
The problem with the blurriness at the end of the loop can't be solved only with focusing. The top third of the fractal has one level less detail than the whole thing, and it's well within the resolution limit of the camera to show that difference. If anything, perfect focus would make the transition point more jarring. Printing the fractal with the same smallest level but three times bigger might not get rid of the problem entirely, but it would be three times less noticeable. You would also need a longer rail or a wider angle lens. Of course, I have no idea if that would make the model too complex to print or even if it would still fit in the printer. Remarkable how good it looks despite this, though! Great job!
Yes, a pinhole could automatically solve the focus and angle of view parts of the problem, but as you say, either a LOT of light or one frame at a time stop motion style.
you'd probably have to first identify the absolute resolution limit your 3d printer is capable of, and then have that limit only used on the 3x smaller copy at the top, and one level less detail on the rest of the fractal, so the before and after shots have the same level of visible imprecision. Though, this might only cover the sides of the smaller copy, as the top of it is another even smaller copy of the whole thing. You could downscale the whole video to 144p to hide the difference in detail at the loop, but then it sort of looks like crap....
Yeah, adding an extra level of detail to the top third would help, but you would still see that extra detail snapping in at the start of the loop, just only on the top third rather than the whole fractal. The difference in detail would also be noticeable between the two parts during the zoom-in. Also, doing it manually one frame at a time for long exposures would be much more time-consuming, and you'd have to calculate and measure the exact position for each shot, but it would also remove the requirement to have a motorized slide altogether.
Good transition match cuts between two objects is hard but fixed with a fade. Good match cuts between takes of the same object is harder. Good match cuts between takes of a physical fractal is pretty amazing.
Wow. I love that you took the time to figure all this out and to share all the details. This really is fascinating. I’ve seen quite a few computer generated fractal zooms, but this is the first real life one I’ve ever seen. Very creative!
I must point out that in cinematography terms at least, this is no longer a zoom. It is a push as the camera is moving towards the subject. Very impressive. If you want to do a zoom-only with a single photo, you would need to position the camera very far away (Perhaps you could jerry-rig a 600mm zoom lens for this) so that the difference between the smaller scale version and the larger scale version perspective-wise is negligible, however the way you have done it is wonderfully cinematic.
Right, as I was hoping, the parallax really adds to it. And of course you’re correct about the terminology. Mathematical terms also get plenty of misuse in contexts with a broader audience - it’s fun to be on the other side this time!
Fractals were a thing that brought me to programming, seeing that effect in real-life is super cool! Very nice work! And I don´t know if this thing has an official name, but your structur is basically a reversed Menger Sponge :)
Ah, the motion control rabbit hole. Surely you considered a follow focus at one point? Also I think having it in reverse, moving out - not in - is an even greater effect.
1:35 I could've sworn this was a moving image, but I pressed pause on the video and it is still gently distorting -- pinching towards the center ever so slightly. Seeing the fractal zoom before it really messed with my eyes. Interesting...
The video loop wasn't perfect, but it's still insanely satisfying. I'm not sure whether it's because the camera gets so close it loses a little focus or if the smallest fractals at the top are so small that the 3D printer can't make them look as defined as the larger ones.
the only imperfection i noticed was the camera and laser not changing focus distance at the same rate as the motion :) the fractal itself is similar to an inverted menger sponge?
it looks awesome with the lazer on it. would be cool to get the camera zoom to keep it in focus the whole time and have a highly detailed pyramid so it looked properly infinite
It seems a similar fractal could be done not based on similarity, but on some other transformation, so that the problem with zooming is avoided (the zoomed projection of part = the projection of the whole, no need to move the camera).
@@henryseg Indeed, I am also afraid it could be a bit boring with only zoom. A third option would be to take advantage of the thing which rotates the model, it so projection = zoomed projection * rotation.
I think I can understand why you didn't also go to the effort of creating an automatic focus adjustment as well, but I think just a touch less blurriness would really sell me on the effect
Very nice! Have you ever printed a fractal in resin? I had difficulty using filament so I used resin and i'll tell you what, It really hit the sweet spot. Not only is it easier to set up but its more refined, strong and when used with a transparent resin it looks just like some kind of crazy crystal from a scifi movie. Due to the fractals transparency I am able to appreciate the underlying order and geometric structure of the fractal. And when exposed to a lazer, bad ass. I even attemted to dope the resin with graphene with no success of it being very conductive. Well anyway this is a big inspiration to me.
This is absolutely insane !! I know it would add a lot more printing time and work but have you considered building a larger fractal pyramid by assembling 9 similar printed pyramids ? You could shoot from farther away, use a different lens, reduce the blur and obtain a greater sensation of infinitely repeating scales.
It would be thirteen smaller prints, and assembling them with the needed precision sounds technically difficult. I guess you could precisely make a metal frame to bolt the prints to. It would be cool to do a bigger, more detailed fractal zoom, but it feels like there are a lot of diminishing returns in this.
The light is in the same position relative to the camera the whole time, other than that the camera is closer to the print. There are differences in shading because the light diffuses through the plastic a fixed distance (which does not scale as we zoom in).
@@henryseg oh I see. Thanks for the reply man. Lol I really was shouting into the abyss anonymously not presuming to tell a pro of this caliber his business.
very cool, though the focus issue is too bad, even if it hides imperfections. Took linear algebra from de Smit 12 years ago, he was still giving popular talks on the droste efffect paper at least yearly!
Freaking awesome! That's a lot of work! I really loved the photographic ones, especially your Esheresque one!🤯 I love surreality, maybe because I'm a little surreal!🤪
@@AR15andGOD Jesus is a mythological character that very likely never even existed! Not even as a crazy messianic cult leader! Your god is not thegodofme, and not even the godofyou, or anyone else! You not only cannot prove he exists, but you can't even show a single shred of evidence for him! You believe by blind faith only, and that's why you have bad judgment, like in thinking you could try to make me look bad, when in fact you are making yourself look bad! Good call fool! Typical of someone who believes themselves to have "God given" morals to show how bad those morals really are!
There is a study performed of a rain forest square area, where they measured each tree, and found a fractal correlation. Your blood vessels in your body branch fractally, as well as many plants grow in a fractal organization. Great video about all the variable considerations. The Last one I could see was the focal point needs to change per the flow as well, but maybe that would make it too much computer generated like.
really well done! In my computer animations of fractal zooms I avoid focusing on the tip but will 'look at'/focuse on a particular point of an iterations surface and then calculate what that point would be on a matching matching surface of the next iteration but different orientation, doing all the same things you did where speed is proportional to distance from the lookat point. If I had a chance to do a project like this I'd love to use a 6dof programable gimble for the fractal. can you get some linear actuators and build a real life hypercube which can rotate along the 6 4d axis next? ;)
WOW amazing visual illusion at 1:35 after seeing the broccoli move when you cut to the white 3d printed fractal it was zooming out and moving (yes I paused to get the full effect)
Interesting how you came to realize you needed a slide dolly. I think most people even photographers think that different lenses (focal lengths, 50mm, 35mm, ect) are what changes the perspective/foreshortening, like if youve seen how different lenses can make a portrait dramatically different, but it’s really not inherent to the lens at all. The main factor is the distance or position of the camera. Different focal lengths are really just different width cones of vision or fields of view, so a crop essentially. So like how you are having to move the camera closer because it is as if you are scaling down the entire world one octave. Great video btw!
I made and 3d printed this exact fractal in my freshman year of highschool a few years back, independantly. I didn't know enough about supports at the time, though, so it has a few still lodged inside of the crevices
Here is a property I think real life fractals would have: at very small scales, the valleys of the fractal approximate the wavelength of light, so on a macroscale some fractals could display structural coloration (like in butterfly wings)
You could demonstrate this using longer wavelength radiation comparable with the size of the smallest detail; this would have to be microwaves or millimetre waves. At the moment I don't think there's any 3D printing technology which has the half-a-micron resolution you would need to get the effect with visible light.
This is such a fascinating idea, coming up with several fractal surfaces and computing the interference and scattering effects involved. Each fractal would likely get its own color and interference patterns. Lovely.
@@zh84 I am sure you can simulate it with ray tracing. I am looking into how to simulate such effects :)
@@incription if you or anyone else figures this out I’d be interested in the results.
there are shorter wave lengths than light though.
As a vfx artist, I love it when people outside the industry run into the issues we deal with on the daily. The perspective discussion in the beginning is something I have very often with directors and cinematographers, even the most seasoned professionals have a hard time understanding why you can't just slap two pieces of footage together without taking all of that into account. To get this perfect you probably need to take lens distortion into account as well, as the edges of the frame can be slightly stretched compared to the center of the image, so when lining up the whole of the image with a different perspective distance, you're can be a fair percentage off from distortion alone because of a largely imperceptible bend. A rectilinear lens can reduce this effect for all intents and purposes, if it's a good one. The final piece to this puzzle would be to motorize the focus so you don't get that artifact as well, and this could also be shot stop-motion style for a perfectly stable and crisp look.
And for the record, I don't think this looks like CG necessarily, you probably could recreate this look in CG, it's just that you wouldn't get this without having this particular photographic reference as a starting point, so it's plausible as CG, but not clearly CG, even the smallest imperfection takes work which is the inverse of what happens in real life photography, so it's actually pretty hard to create a photo that definitely looks CG, it has to be extremely exact, it's an artform in itself.
The issue of lens distortion is something I’ve been leaving in its can (with all the other worms) and trying to not think about!
You’re right that it doesn’t look that much like CG, which is probably for the best. I’ve run into the issue more with stills, like my current avatar photo (illustrating stereographic projection). With video, there are so many more things to notice.
Is the lens distortion causing the visible perturbations in the Romanesco broccoli?
Change in Depth of field and focus seems to be a problem also
@@Hexnilium I doubt it - Feliks uses only one or two photos for his zooms, and no single photograph would look distorted like that.
Couldn't you bypass all of this by placing the camera far and using a zoom? The perspective difference would be tiny.
It seems like the loss of focus is being used to help hide the loop, which is clever, though it would be really cool to see one that stays in focus too! Phenomenal video
I’m pretty sure that the blur is only there to prove that it’s not computer generated, as he mentioned he left mistakes in for that reason. I also wish that it didn’t go out of focus because then I’m pretty sure it would be perfect
@@christophermoore6110I was half joking about the mistakes. I’m still far enough from perfection on these loops that there is plenty of room for improvement.
@@henryseg really? The only mistake I personally noticed was the blur lol
The blur for me was what kept telling me it was a loop :/
I'd rather see the imperfections as you get closer in high fidelity and transition to the farther image than rely on blur if it was one of the "intentional mistakes" (which I doubt). Even with the out of focus shot you could start the transition between loops earlier to hide the blur, but then you lose more of the sharp frames and also the video would become mostly edited instead of mostly real footage
@@henryseg
idk if you can motorise the focus or if autofocus is accurate enough to go the right way without overshoot, or if focussing on infinity is possible.
I wouldve suggested using a "camera" that can capture orthographically (therefore you can forego the whole rail setup entirely and zoom digitally) but the perspective..uh perspective..is a really cool way to convey the shape
I suspect that the camera may get closer to the fractal than its lens' minimum focus distance, which causes the blur. Or perhaps it's set to manual focus and that's why it gets blurry. It might have been interesting to see a camera with a longer telephoto lens set further back from the fractal and turn on auto focus with the center of the sensor as the focal point.
I loved that you showed the problem solving process. I can appreciate the loop more knowing the effort that went into it.
Amazing work! It really does look like CGI. I wonder how close you could get a natural fractal to behave like this, like with a fern leaf or broccoli. Less precise than a 3D print I assume, but the detail is better than the print resolution, so it wouldn't look as blurry.
The closest I've seen to something like this is by John Edmark, see www.johnedmark.com/natural-blooms-1.
@@henryseg Nice!
the blur isnt from the object being 3D printed, its from the camera moving closer but still having the same focal length so the object starts to get blurry. If he could also change the camera focus as it slid forward he could make it look much better, and then the 'revert to start' part wouldnt be as obvious as it is now
@codeparade funny seeing you here
@@SpydersByte It's both, you can see that the 3d print only gets so detailed. If there was no blur the lack of fine detail when zoomed in would be more obvious.
This should become a videography hobby in and of itself. The end product really is stellar and you did a good job overcoming the challenges that can arise from this kind of work that requires precision and accuracy. 😁
It is neat how doing it in real life rather than with post processing in software from a photo removes that weird uncanny artifact of smudging. The two products next to each other would not even have a contest because this is in a league of its own.
there already is a whole community who are loopers
The closeness blurs let on to the reality better than the hand and laser, to be honest. This is such an awesome idea and execution!
yea, although it would look better without the blur lol
He actually mentions it at 8:05
@@TtEL Doesn't make sense though, he proves it through other means. The blur breaks the illusion unfortunately
Should have used a macro lens
The exponential slow down as you zoom makes so much sense, that explains why my 3D fractal zooms always felt like they were timed wrong- thank you!
The fact that the linear speed has to be exponential while the rotation speed has to be constant, is another clever reminder of the complex relationship between sinusoids and exponentials.
Are you willing to elaborate?
@@adi-ow1cg You should look up Euler's identity. It shows how if you think of x as being some angle in radians then e^(ix)=cos(x)+isin(x). The relation is probably much deeper than this but i think this is what they are referring to.
Rotation speed doesn't have to be constant.
The camera motion is in a completely different axis to the rotation speed, so no wonder rotation speed is irrelevant.
But the orientation at the end of the loop must match as it was in the starting if the images are to line up. That can be achieved even with chaotic rotation.
@@adiadiadi333 Sure, there's no constraint on the absolute speeds of either component, but the relationship between rotational and linear speeds definitely is constrained.
@@AJMansfield1 impressive
MOST IMPRESSIVE
As ever, your videos are among the most consistently, singularly interesting UA-cam content
1:46 this is the first video i've ever seen that understands that yes, 2d worlds have parallax!! you don't need to have a fog or have objects glow to discern depth in 2 dimensions, you can judge distance by the width of things alone- THANK YOU
I was really excited for this because I recently printed a fractal of the Sierpinski triangle and it's one of my favorite prints. Printing fractals is one of my favorite uses of 3D printing as a beginner.
You could potentially coat the model to reduce the subsurface scattering that is occurring after zooming in. Also, a point source light could reduce the scale variance in the lighting.
There's a diy fake window that uses fresnel lenses and soapy water that would go great here, plus some dynamic focusing
The continous loss of focus unsettles me on some deep level. Gets my skin crawling to a point where I just want the perpetual loop to end as soon as possible.
i like the transition between blur and clear focus. it also adds to the computer-generated look by making it look like the next fractal iterations are loading in
This is incredible. Sometimes what can seem like a really basic shot to a complete amateur (like me), can teach you so much about how it was made, and why there’s nothing basic about any part of this shot. There’s so many cool things about this print, and so many problems in creating this, that I would never have appreciated if I just saw the loop alone. It’s analogous to a fractal itself. The more you look, the more you see. It just goes deeper and deeper and deeper.
There are many videos i have watched on youtube, but this is quality. I can tell I"ll be coming back to rewatch this ,thanks for detailing your process, legend!
The laser illuminating the fractal makes it so much cooler.
The subsurface scattering of that laser with the printed material is just luxurious.
oh man this is cool, watching the blurry one fade into a sharper one is so satisfying
What a madman! It's unfathomable the size of his brain just to get the animation recorded and edited, but to explain the process and all the related concepts? My god
Beautiful and brilliant, right down to the precise duration of the final laser-lit loop.
There was a fun juxtaposition between how serious your voice sounds and describing that little clamp as "cute".
Fascinating work! If you have a camera with manual focus adjustment you can get a perfect focus for the whole movement like how the movies use a person doing it manually called focus puller.
It always amazes me when a person has the patience for such things.
Great work. I'm nerding out so hard!
dude. youre a genius
Ive tried to do a simple animation loop in my comic "hole" and cant do it properly and its just a 2D drawing!!
youve dome it with a 3D PHYSICAL OBJECT!! its amazing!
The way the structure is, it really seems like you could play with many ways of lighting the piece up. To highlight & contrast the textures of the design.
So cool! I love the fractal in the dark with the laser at the end!
Learning has never been more accessible, thank you for taking the time to make this amazing video. Quite inspiring!
1:06 I got an existential shiver when you said 2003 was a little over 20 years ago 😅
Tell me about it…
While moving the camera is the only way to perfectly replicate the dimensions of the fractal, it would probably be close enough to use a long focal length (the longer the better) and then do a digital zoom. Once your focal length gets long enough you may as well have an orthographic camera, and this technique has been used for some other real life illusions that require an orthographic perspective.
Yes, although then the effect wouldn’t look as good. You wouldn’t get any parallax effects as we fly over features.
Great walkthrough on how you made it and the end result was awesome!
The problem with the blurriness at the end of the loop can't be solved only with focusing. The top third of the fractal has one level less detail than the whole thing, and it's well within the resolution limit of the camera to show that difference. If anything, perfect focus would make the transition point more jarring. Printing the fractal with the same smallest level but three times bigger might not get rid of the problem entirely, but it would be three times less noticeable. You would also need a longer rail or a wider angle lens. Of course, I have no idea if that would make the model too complex to print or even if it would still fit in the printer. Remarkable how good it looks despite this, though! Great job!
Yes, a pinhole could automatically solve the focus and angle of view parts of the problem, but as you say, either a LOT of light or one frame at a time stop motion style.
you'd probably have to first identify the absolute resolution limit your 3d printer is capable of, and then have that limit only used on the 3x smaller copy at the top, and one level less detail on the rest of the fractal, so the before and after shots have the same level of visible imprecision. Though, this might only cover the sides of the smaller copy, as the top of it is another even smaller copy of the whole thing.
You could downscale the whole video to 144p to hide the difference in detail at the loop, but then it sort of looks like crap....
Yeah, adding an extra level of detail to the top third would help, but you would still see that extra detail snapping in at the start of the loop, just only on the top third rather than the whole fractal. The difference in detail would also be noticeable between the two parts during the zoom-in.
Also, doing it manually one frame at a time for long exposures would be much more time-consuming, and you'd have to calculate and measure the exact position for each shot, but it would also remove the requirement to have a motorized slide altogether.
Dude, this is so freaking cool! Seriously, this is way too rad.
This is so cool. Thank you for sharing. Also, your voice is really nice to listen to for a long explanation. Thanks for the narration
8:40 Shoutout to the cutest clamp of all time being how my Vive Basestations are held for VR lol.
There's an awesome work being put on this video. From the perspective explanation to the exponential zoom.
I don't get how it only has 200k views.
Good transition match cuts between two objects is hard but fixed with a fade.
Good match cuts between takes of the same object is harder.
Good match cuts between takes of a physical fractal is pretty amazing.
the ending footage with the laser is super cool and mesmerizing
Wow. I love that you took the time to figure all this out and to share all the details. This really is fascinating. I’ve seen quite a few computer generated fractal zooms, but this is the first real life one I’ve ever seen. Very creative!
Very nice project! I love the infinite zoom on the picture you made you showed at the begining
I must point out that in cinematography terms at least, this is no longer a zoom. It is a push as the camera is moving towards the subject. Very impressive.
If you want to do a zoom-only with a single photo, you would need to position the camera very far away (Perhaps you could jerry-rig a 600mm zoom lens for this) so that the difference between the smaller scale version and the larger scale version perspective-wise is negligible, however the way you have done it is wonderfully cinematic.
Right, as I was hoping, the parallax really adds to it. And of course you’re correct about the terminology. Mathematical terms also get plenty of misuse in contexts with a broader audience - it’s fun to be on the other side this time!
Fractals were a thing that brought me to programming, seeing that effect in real-life is super cool! Very nice work!
And I don´t know if this thing has an official name, but your structur is basically a reversed Menger Sponge :)
Ah, the motion control rabbit hole. Surely you considered a follow focus at one point?
Also I think having it in reverse, moving out - not in - is an even greater effect.
I got focus pulling sorted out in the follow up video: ua-cam.com/video/uH8w7I1Og1I/v-deo.html
Never stop doing what you do!
Beautiful effect! This video plus the 3d print would make for a great museum piece.
1:35 I could've sworn this was a moving image, but I pressed pause on the video and it is still gently distorting -- pinching towards the center ever so slightly. Seeing the fractal zoom before it really messed with my eyes. Interesting...
The video loop wasn't perfect, but it's still insanely satisfying. I'm not sure whether it's because the camera gets so close it loses a little focus or if the smallest fractals at the top are so small that the 3D printer can't make them look as defined as the larger ones.
Your videos are always such a delight.
You make some of the coolest videos out there, thank you man!
videos like this restore my faith in humanity
the only imperfection i noticed was the camera and laser not changing focus distance at the same rate as the motion :)
the fractal itself is similar to an inverted menger sponge?
Stunning work!
Amazing work all around. Truly stellar
it looks awesome with the lazer on it. would be cool to get the camera zoom to keep it in focus the whole time and have a highly detailed pyramid so it looked properly infinite
It seems a similar fractal could be done not based on similarity, but on some other transformation, so that the problem with zooming is avoided (the zoomed projection of part = the projection of the whole, no need to move the camera).
Interesting, although the parallax changes as the camera moves in are one of the things I like about this zoom.
@@henryseg Indeed, I am also afraid it could be a bit boring with only zoom. A third option would be to take advantage of the thing which rotates the model, it so projection = zoomed projection * rotation.
I really appreciate the time and effort you put into your videos. Thanks!
I think I can understand why you didn't also go to the effort of creating an automatic focus adjustment as well, but I think just a touch less blurriness would really sell me on the effect
Really cool video. Though I'd still like to see it done with other fractals or maybe a very high res 3d print so the loop looks more seamless
i love fractals because it gives a glimpse of what the universe looks like
This legit looks so mesmerizing. So cool that you could do this without any of the distortions! 😊👍👍
So, so cool, and so well done!
Great work! Kinda trippy seeing an "real" fractal object in a video
ah man the exhibition real life photo zoom is INCREDIBLE.. I am so happy you let me see that, thank you.
*I'm..... so high rn...... and this is like therapeutic af my g*
"but have you ever seen a real life fractal zoom?"
Laughs in psilocybin
Very nice! Have you ever printed a fractal in resin? I had difficulty using filament so I used resin and i'll tell you what, It really hit the sweet spot. Not only is it easier to set up but its more refined, strong and when used with a transparent resin it looks just like some kind of crazy crystal from a scifi movie.
Due to the fractals transparency I am able to appreciate the underlying order and geometric structure of the fractal. And when exposed to a lazer, bad ass. I even attemted to dope the resin with graphene with no success of it being very conductive. Well anyway this is a big inspiration to me.
That was insane! It was hard for my head to believe it was real
This is absolutely insane !! I know it would add a lot more printing time and work but have you considered building a larger fractal pyramid by assembling 9 similar printed pyramids ? You could shoot from farther away, use a different lens, reduce the blur and obtain a greater sensation of infinitely repeating scales.
It would be thirteen smaller prints, and assembling them with the needed precision sounds technically difficult. I guess you could precisely make a metal frame to bolt the prints to. It would be cool to do a bigger, more detailed fractal zoom, but it feels like there are a lot of diminishing returns in this.
@@henryseg Yeah I realized that you also would need to print 6 vertical sides.Thanks for the answer anyway and I'll keep an eye on your work !
This is some amazing dedication, really great work!
Need a ring light as a halo right above the print then the lighting would stay even from all perspectives because the shadow shifting is a tell
The light is in the same position relative to the camera the whole time, other than that the camera is closer to the print. There are differences in shading because the light diffuses through the plastic a fixed distance (which does not scale as we zoom in).
@@henryseg oh I see. Thanks for the reply man. Lol I really was shouting into the abyss anonymously not presuming to tell a pro of this caliber his business.
So glad you did the loop with the laser. I was wondering if that'd be possible!
very cool, though the focus issue is too bad, even if it hides imperfections. Took linear algebra from de Smit 12 years ago, he was still giving popular talks on the droste efffect paper at least yearly!
0:10, Now I really want to live in a Fractal castle
That is so fun! I'm glad you were able to make it work!
Bro the laser looks so cool I love it omg
This looks like an ancient-future technotemple.
That very last shot is sick
Brilliant work! Your channel deserves faaar more Subs, Views.
That 3D Koch flake is just incredible! :O
That's pretty cool, I like it!
Freaking awesome! That's a lot of work! I really loved the photographic ones, especially your Esheresque one!🤯 I love surreality, maybe because I'm a little surreal!🤪
Stay away from shrooms kids
@@AR15andGOD Jesus is a mythological character that very likely never even existed! Not even as a crazy messianic cult leader! Your god is not thegodofme, and not even the godofyou, or anyone else! You not only cannot prove he exists, but you can't even show a single shred of evidence for him! You believe by blind faith only, and that's why you have bad judgment, like in thinking you could try to make me look bad, when in fact you are making yourself look bad! Good call fool!
Typical of someone who believes themselves to have "God given" morals to show how bad those morals really are!
The fractal kinda looks like a visualisation of the Collatz Conjecture where any odd number is multiplied by three and added to one!
Fantastic!
Was it just me or 1:38 when it goes from the broccoli zoon to your 3D print, the print looked like it was moving?
There is a study performed of a rain forest square area, where they measured each tree, and found a fractal correlation. Your blood vessels in your body branch fractally, as well as many plants grow in a fractal organization.
Great video about all the variable considerations. The Last one I could see was the focal point needs to change per the flow as well, but maybe that would make it too much computer generated like.
Really cool effect! That must have taken a lot of work to get the timing just right.
really well done! In my computer animations of fractal zooms I avoid focusing on the tip but will 'look at'/focuse on a particular point of an iterations surface and then calculate what that point would be on a matching matching surface of the next iteration but different orientation, doing all the same things you did where speed is proportional to distance from the lookat point.
If I had a chance to do a project like this I'd love to use a 6dof programable gimble for the fractal.
can you get some linear actuators and build a real life hypercube which can rotate along the 6 4d axis next? ;)
Saw the final video on mathstodon and I’m so amazed to see the work for it!
I love how the coastline zoom has smaller and smaller roads and buildings
the zoom in doesnt account for focus which kind of breaks the illusion, amazing work
Very cool! FYI the camera move you want is actually hyperbolic in the form y=1/(mx+b), not exponential.
Actually, it is exponential.
@@MichaelDarrow-tr1mn No, there's an asymptote so it's hyperbolic.
Wow that looks really cool. If the blur wasn't there, it wouldn't be distinguishable from a simulation
WOW amazing visual illusion at 1:35 after seeing the broccoli move when you cut to the white 3d printed fractal it was zooming out and moving (yes I paused to get the full effect)
Interesting how you came to realize you needed a slide dolly. I think most people even photographers think that different lenses (focal lengths, 50mm, 35mm, ect) are what changes the perspective/foreshortening, like if youve seen how different lenses can make a portrait dramatically different, but it’s really not inherent to the lens at all. The main factor is the distance or position of the camera. Different focal lengths are really just different width cones of vision or fields of view, so a crop essentially. So like how you are having to move the camera closer because it is as if you are scaling down the entire world one octave. Great video btw!
The issue with this is that you can tell when the loop restarts. But kudos for doing all the work to get it as good as you did.
Damn cool. So much problem solving going on throughout the video. Kudos to your ingenuity
great final result... i really want to try an recreat this in blender now
I made and 3d printed this exact fractal in my freshman year of highschool a few years back, independantly. I didn't know enough about supports at the time, though, so it has a few still lodged inside of the crevices