 blooms, you know, Google that, blooms. And he gave a very wonderful talk at Bridges. I can't resist showing you the picture of the Sierra Gooseberry because where I go to the Sierra Nevada, our gooseberries have thorns all over them. And yeah, you get thorns in your fingers when you pick them and make them into beautiful jelly. But what I'm going to show you is that this Fibonacci spiral, it's not just any old spiral. It's got to be this special thing involving Fibonacci numbers, though, like, let me draw your attention to that motif or that little piece of the figure. And then when I rotate through this special golden angle, it becomes just slightly larger, right? So I've got, you know, the pattern, a little piece of the pattern turns into a slightly larger piece of the pattern. So if I were to strobe this, it would appear that the pattern was emerging and coming out at me like that. That's where you're supposed to say, ooh. And it works in shapes, too. So this is a wallpaper pattern with hexagonal symmetry used to make a little virtual object. Now, I actually have a real object, a real copy of this in my bag, if you want to see it afterward. This is all done in maple with just, you know, creating this strobing effect. It looks for all the world like that is blooming and emerging. You can also see when these Fibonacci spirals are happening, it's like they're coming out of the bottom of the Riemann sphere and into the top of the Riemann sphere. So, you know, the plane is in the plane, they're just going out. But if you bring the plane around to be the Riemann sphere, they're coming into the top. Well, it's a simple transformation to just, you know, a merriest transformation to bring the North Pole to a finite point. And the strobing effect still works, as I was delighted to find. Now, we come back to the idea that when you've made wallpaper, each wave knows how to move itself into the future. This past year, I had an extraordinary opportunity to coordinate with the San Jose Chamber Orchestra. They commissioned a composer named Bill Sussman to write music to go with my movies of vibrating wallpaper. I have a five minute video that appears on YouTube, if you'd like to see. You can probably find the link fairly easily. Now, I think that when I press the button, this is going to start vibrating, and we're going to hear the music. So, people in the sound, ready? Okay, well, we will have to imagine the beautiful sounds of strings here and this vibrating wallpaper effect. It's just, it's finding different pixels there, and there is, again, something beautiful and platonic about this motion because it is connected to the linear wave equation. That's my theory and I'm sticking to it. Now, I'm not quite done. I just wanted to say there are many, many more spaces to explore and I know that all of you are here on a wonderful adventure at the Park City Mathematics Institute. So, I would love to think that some of you are going to become creators of wallpaper, but also maybe some of you are going to investigate the artistic potential of function spaces that I didn't even think of. So, what are you going to find in these spaces of functions for mathematical art? Thank you. Thanks very much, Frank, that was a lovely talk. There's some time for some questions. Anybody has? Okay, well, Frank is gonna be, oops, Paul? Maybe six slides before the end when you were rotating and it was coming out at you. Yeah, maybe this one. What happens if you accelerate the rotation? Well, I could certainly do more frames per second and then there's this issue of, it's kind of complicated. This is a 21 frame thing where I'm not really using the perfect golden angle. I'm using a ratio of two successive Fibonacci numbers instead so that it'll match in the time loop. So, you use higher order Fibonacci numbers. You can get a tighter spiral. It'll look more like it's zooming out at you. You use the coarser ones. It'll look a little more chunky. This one is sort of a compromise. This one, that's really good, isn't it? It does not look like continuous still motion. But yeah, I could, so, does that help? I was just thinking of the original Star Wars. Yeah, I could make that happen. Other questions? Other questions? Okay, well, Frank will be here. Through Thursday night and I encourage you to go up and find him. He'll be very happy and he'll be leading some of these part of the Experimental Math Lab which we'll be meeting to organize tomorrow. So, thanks again, Frank. Thanks.