IRA FLATOW: To best describe this next story, you need to imagine an artichoke, an artichoke. Now visualize putting that artichoke on a turntable with its stem right in the center spindle. Now that’s set up in your mind, get the center spindle turning.

You flash a strobe light. As it’s spinning– and if you spin the artichoke and flash the strobe at the right speed, the artichoke leaves will look like they are growing, that they are animated. And the secret to this phenomenon– it’s math, of course– something called the golden ratio.

There is an art, an artist creating sculptures based on this math and on this effect. Our video producer Luke Groskin is here to get to the artichoke heart– sorry, Luke– of the matter. It’s the subject of our latest video.

And if you haven’t seen the video yet, you have to check this out at sciencefriday.com. Luke has done great videos. But this one is a mind-bender.

LUKE GROSKIN: It’s mesmerizing.

IRA FLATOW: Yeah. That’s right. You sit there. And you look at this.

LUKE GROSKIN: You can watch it for a very long time. It has– and that’s kind of the point. It’s animations of sculptures that are never-ending.

IRA FLATOW: So why does it look like it’s blooming based on this golden ratio?

LUKE GROSKIN: OK, so there’s a lot of things that impact to understand how these are blooming. So this is the work of John Edmark. And the sculptures you’re referring to are what he calls his bloom series. And it looks like it’s blooming, because he’s constructed them like a frame of animation, like a single cell of animation.

So each side of it is he’s placed the different elements of these blooms– again, they look like a artichoke, a head of an artichoke, or a cactus, or sometimes these kind of abstract, like koosh ball kind of shapes. And he places each of the elements based on what you described before, the golden ratio, more specifically the golden angles. So we’ll say the spiral form of the golden ratio.

And each of those elements, when it’s spun around– and we’re using a strobe, like a light strobe– you only see one specific element at a time. But he’s placed them in such a way that it looks like they’re moving. And depending on how far away from the golden ratio, the golden angle he places them, he can get them to move and wiggle and kind of finesse and vibrate. It’s really mesmerizing.

IRA FLATOW: So I see you need that flashing strobe to sort of capture the movement or create the animation part.

LUKE GROSKIN: Yes, either that or you need to set your camera shutter to be to be very really, really high if you’re taking this on video. You have to set your shutter that way.

IRA FLATOW: Sort of like the wagon wheels on the trains in the movies. They spin around.

LUKE GROSKIN: Exactly.

IRA FLATOW: The shutter is flashing.

LUKE GROSKIN: Exactly. So you can get the sensation that it’s not moving in that case or that it’s moving very slowly, when in fact it’s moving very fast. He’s manipulating the kind of rotation like that. But in this case, he’s making these blooms that look like they’re constantly in motion. And the motion never ends.

IRA FLATOW: And so he likes spirals. He’s chosen spirals.

LUKE GROSKIN: Yes. Spirals are kind of his inspiration. They have this powerful geometric– this powerful geometry. And they also have this beautiful static, but it’s more than that. There’s a philosophy behind his use of spirals. This is how John Edmark describes this kind of fascination.

JOHN EDMARK: Spirals make reference to the fact that you can never return to the same place again, that nothing ever does truly repeat. It goes infinitely small. And it goes infinitely large. It’s endless.

And you know, we sort of don’t know where we came from. And we don’t know where we’re going. And we’re just sort of this a piece of that larger picture.

IRA FLATOW: Describe for us what the spirals look like when you make them.

LUKE GROSKIN: Well, they come in many forms. And if you go to his studio, you see these kind of wooden towers that are built up of all these layers. And he can manipulate them one layer at a time at exactly 137.5 degrees, the golden angle. And it creates this kind of beautiful motion.

He also has these kind of childlike toy inventions that he’s made called the lollipopter, that starts off as like a DNA helix. And just with a flick of the wrist, it suddenly becomes this kind of little wooden Christmas tree kind of like structure. And you can hold it in your hand.

He has these spiral tentacles that are made of wood that he can just by expanding, or contracting, or pulling a lever, they kind of unfurl. So the spirals, and the geometry, and the mathematics are just everywhere. You can experience it throughout all of his work.

And then, of course, there are these 3D printed blooms, which are crowding a desk, a table. And they’re just coming so many different shapes. And they don’t look like any. They’ve just look like gorgeous little statuettes. But when they move, man.

IRA FLATOW: And you spin them around.

LUKE GROSKIN: Yeah.

IRA FLATOW: I’m Ira Flatow. This is Science Friday from PRI Public Radio International, talking with our video editor Luke Groskin about the spirals. So he makes each one of these by hand. Does he 3D print them? How does he make them?

LUKE GROSKIN: So he uses them– he designs them on a computer. And he places all the elements on a computer. You could not achieve the level of symmetry, and perfection, and detail work by hand. You just couldn’t do that.

So everything is done by computer. And then exports and puts it into a 3D printer. And he prints out these blooms. And then in the case of, say, his wooden, kind of more wooden structures, he actually ends up basically laser cutting them out of wood.

IRA FLATOW: Wow. It’s amazing. And, of course, we can see this golden ratio in nature besides just the–

LUKE GROSKIN: Yes, yes.

IRA FLATOW: –artichoke we have.

LUKE GROSKIN: Yes. So if you know about this ratio, this famous golden angle or the golden ratio, it’s really famous. If you look at a Nautilus shell, that is a shell, that structure, that follows the golden angle. And if you look at, say, you know, galaxy formation or like what we’ve talked about artichokes, or my favorite is the Romanesque broccoli–

IRA FLATOW: Broccoli?

LUKE GROSKIN: Yes.

IRA FLATOW: Spinning broccoli?

LUKE GROSKIN: Well, it looks like this fractal broccoli. You can find at a farmer’s market, usually. And it’s this– if you spin that, then you get that sort of structure.

IRA FLATOW: All right. Let’s go to the phones. We have a caller at two. Let’s go to Michael in Cincinnati. Hi, Michael.

MICHAEL: Hey, Ira, wonderful to be on.

IRA FLATOW: Thank you. You’re Welcome.

There are– I’m an engraver. And I run tools called rose engines. There are weights that have rocking spindles. And we engrave– think of pocket watches. We engrave probably the most common pattern. It’s called a barley, after a barley or wheat, where we’re recording equal radios from the center out.

And it imitates– it’s not fibonacci. It’s not that actual, but it imitates and looks very much like what you’re talking about. And the light moves around on the engraving anytime you move at equal radials.

There’s also a great video of a guy with a bowel, a potter’s wheel. And he paints wet slip into it. And then as it’s spinning, depending on the speed as he drags his finger up and down, he gets the same strobe effects that you’re talking about. It’s just– it’s absolutely mesmerizing.

IRA FLATOW: Wow. Well, thanks for calling.

LUKE GROSKIN: Yeah. It’s a very– using math, and using spirals, and using this kind of naturally curling geometries can have some really powerful aesthetic effects. And when John Edmark was talking about this, he talked about his kind of his inspiration and how it’s not like spinning an artichoke has never happened. And it’s not like nobody knew that there weren’t spiral structures on an artichoke.

And that’s where his joy comes from is kind of discovering that if he just puts a camera there and he spins it on a leaf, he can do that. He can create that. And then he can recreate it in his own work.

IRA FLATOW: And he sells his artwork. You can buy it if you wanted to.

LUKE GROSKIN: Yeah. You could buy it. I think you can actually 3D print it if you go to his web site johhedmark.com.

There’s ways to actually make it yourself. And you can actually buy these structures. And yeah, it’s pretty cool. And if you don’t if you don’t have the money for it, then absolutely check out the video.

IRA FLATOW: The video is up on our web site?

LUKE GROSKIN: Yeah, it’s on sciencefriday.com. And if you like our videos, then you can become a monthly supporter now of our videos. Become a patron. It’s right there on the video page.

IRA FLATOW: That’s great. Luke Groskin, thank you very much.

LUKE GROSKIN: Thank you.

Copyright © 2017 Science Friday Initiative. All rights reserved. Science Friday transcripts are produced on a tight deadline by 3Play Media. Fidelity to the original aired/published audio or video file might vary, and text might be updated or amended in the future. For the authoritative record of ScienceFriday’s programming, please visit the original aired/published recording. For terms of use and more information, visit our policies pages at http://www.sciencefriday.com/about/policies/