2021年国際数学アートコンテスト入賞作品

At first glance, this appears to be a static graph, but look a little deeper and you’ll notice the wagging of the cats’ tails, the ticking of the clock, and the oscillations of the screensaver. The most striking thing is that each cat is unique not just in its apparent coat and color, but in its mathematical nature: each is outlined by a different class of functions, including linear, parabolic, cubic, exponential, logarithmic, sine, arcsine, elliptic, and Bezier curves. A mathematical and creative tour de force.

I was inspired to make this graph by the idea that cats have nine lives, with every cat in this scene being made entirely of a different kind of equation. I also made the vanishing point of the room (0,0) so I could also play with perspectives. This project was especially challenging for me as I had to master a variety of equations and learn the basics of perspective all in under a week.

Perhaps you first noticed the shadowy representation of a person sitting at a piano. Or maybe the subtle animation of the notes coming out of the piano. Maybe it was the rich background texture from a complicated implicit expression, or the wavy morphed ellipses that form the reflection in the water. Or maybe it was the audio trace on line 2 that plays the entirety of Beethoven’s “Moonlight Sonata.” Wherever you look, you’ll find layers upon layers of interesting and beautiful mathematics.

I recreated one of my paintings of a moon and a person playing the piano and turned it into a multisensory experience using the Desmos Graphing Calculator. I explored and learned how to create animations and use the audiotrace feature to create music.

The judges were struck by the impeccable use of color, line thickness, delicate shading, and the appearance of motion. Dynamic colors are used sparingly but effectively, highlighting the digital station sign and the few shards of glass. Overall, a visually stunning piece that combines many different features of the calculator into a truly original creation.

I've always had an innate passion in trains during my childhood. Throughout this journey, I have learnt a myriad of techniques including colour-changing objects and Bézier curves, which I then integrated into this piece with the focus of a vanishing point.

This graph blew us away with its blazing-fast performance, incredibly concise expression list, and charming graphics. At Desmos, we all love a well-organized graph with clearly named variables and well-organized folders. The judges also admit to spending a little too much time playing this delightful game.

I made this graph to commemorate my love of skiing, which I haven't been able to satisfy while living abroad in Djibouti and Taipei during the past few years. I wanted to create a simple, fun, and challenging skiing game in Desmos using what I've learned while interacting with the Desmos community over the past year, and I used the default Desmos colors to make the game "feel" like Desmos. The greatest challenge was trying to make the game appear the same on all devices, creating the need for device calibration.

Ammonite is a seamless blend of sophisticated mathematics and nuanced artistic expression. Each component contributes to its wildly immersive environment. The creature is brought to life by the natural-looking striping on the shell with random mottling and uneven spacing, the organically rippled gradient of the background seascape, the undulating tentacles in the ocean depths. We also love the web of segments and points that cleverly and thematically mimics the look of a net.

My artwork is a creature with a spiral shell and tentacles moving underwater. I have been fascinated by objects from the sea, especially the spiral shells of mollusks, so I choose to create an ammonite whose shell can be easily modeled using parametric equations. I use this opportunity to explore the limit of the calculator to create a three-dimensional object that displays realism, while I intended that viewers can easily recognize the mathematical primitives.

Earth Woman uses a variety of expression types to create a spellbinding artistic masterpiece. She is the forest manifest. Her sinusoidal hair billows with the colors of lush foliage, and her face is adorned with vines and blossoms. We were charmed by the subtle glow and hovering motion of points flying around like little fireflies. Don’t miss the rainbows in her irises. The layering of line opacity and thickness is a lightweight and effective solution to create the illusion of light reflecting off the skin. This piece captures the power and beauty of nature in a portrait of a woman.

My project was inspired by different illustrations and depictions of “Mother Nature/Earth”. I took the desmos art contest as an opportunity to create my vision of this mythical personification of our planet. While doing so I also learned more about animating on Desmos, and how to best use the different parent functions to create detailed line art.

We love it when we discover that an exceptional piece of graph art in our finalists began as another, equally impressive, but stylistically different piece of art. Deviating from the realism of her original pencil drawing, Sheila completely embraced this new canvas to create a fresh and striking new oeuvre. The thoughtful layering of irregular polygons and opacities construct an abstract but legible composition full of depth and volume. The subtle movement in the shimmer on the ketchup and the changing colors of the background bring a whimsy to this piece that would have been lost in other mediums.

What will realistic art look like when expressed abstractly? With this thought I drew one of my realistic food art "Euphoria" again using desmos. Focusing on the structure of the fries and the overall appearance rather than the texture and the details, the new art echos but differs from the original.

The Desmos-in-Desmos calculator is out of this world. It is a true feat of design that uses all tools available to make this both performant and expansive in what it can do. Enjoy graphing your own expressions, or try clicking on the die to get a random pre-loaded graph. We had great fun testing the limits of what this very meta-calculator can do, and encourage you to as well.

I drew inspiration for this project from one of my favorite works of art: the Desmos Graphing Calculator itself. This graph is the culmination of months of tough design designs, trade-offs, and hard work. Throughout the process, I learned about architecting, building, and iterating such a huge project with a focus on performance.

This graph takes advantage of nearly all the ways Desmos can be used to create shapes. There are polygons building up the shadows on the mountain, inequalities filling in a gradient of snow on the slopes, and a hue of blue for the ski lift windows. The trees come from vertical sinusoids, while the frame around the entire scene is decorated with explicit equations of lines. Parametric paths provide a way down the mountain for each individual skier, themselves simple images created in an earlier graph. As beautiful as the view is from afar, zooming in reveals new details and delights—who knew a skiing cow could face such peril? Hit play, sit back, and enjoy the cycle; then zoom in and watch it all again!

Creating this animation took me back to the days I spent volunteering in Switzerland; I tried to stay true to that through the mountain background based on a photo I took, the snow piled high on the roofs of chalets, and the animation. I applied periodic and parametric functions to create hundreds of trees, and to animate the chairlift and skiers so it is seamless, even when the slider loops back to the beginning. To animate the pieces seamlessly, I created the images of the skiers and chairs using lines and polygons, exported them as images to animate them both individually and using lists, which helped me to create the working chairlift and the skiers on the slope.

Blooming Flower planted a seed in our hearts that grew with each passing scene. Outside of Desmos, the story told here would be an engaging narrative. Within the confines of a graphing calculator, it becomes an impressive display of planning and positioning. The artist even found a wonderful technique for saving calculator resources by disabling unnecessary expressions, a key technique that allows the full story to be appreciated! Set aside some time to watch through this engaging tale.

I always want to tell a story by animation in Desmos, and see if it can render in normal speed (24 fps), therefore I gave it a try. I learned various ways to optimize the performance, some usages of list and action, animation technique, developed much deeper understanding about Bezier curve and so much more.

At their core, every graph in the Cartesian plane is simply a collection of points. In this submission, we see those points cleverly positioned and animated to give the illusion of a thee-dimensional wave of water racing to meet the wind on a sun-filled shore. Like many great works of art, there is a message waiting to be experienced here—we encourage you to jump into this graph and play around with the controls. Can you find a beach you would be happy to immerse yourself in?

While experimenting with 3-dimensional points, I got inspired to make this tiny beach. For me the smooth running 3d animation was the most important factor, so I only have one list of displayed points. Changing the year shows how trash can ruin the idyllic beach.

Part of the wonder of mathematics is that it provides a common language with which we can model the world. Desmos provides a particular dialect of that language, as do other tools like Python (a programming language) and Blender (a 3-D modeling software). For this submission, the artist leveraged the common mathematical foundation in each of these tools to once again push the boundaries of what we think is possible to create with Desmos. From lighting effects to character rigging to sorting polygons for occlusion, this graph is a wonderful integration of so many different techniques. Click through to the pre-recorded “Featured Animation” to see the character move about the scene.

I wanted to tell a story about a man who drank too much sinusoidal milk. For this graph, I learned about facial animations, motion outputs, vector graphics, UV textures, Desmos' API, Blender, Python, and much more! I also learned about the five megabyte graph limit. :)