This is my algorithmic love letter to a forefather of mathematical art: **M. C. Escher**.

To commemorate 125 years since his birth, my goal was to honor Escher’s enduring influence by reworking his iconic motifs into a medium that embraces mathematics as much as he did.

I gave it the name **Escherly Seeds** because its meaning is three-fold:

-	_Metaphorical._ This work can be seen as representing the seeds that Escher planted in the minds of the artistic community, and I make several references to his work. Concave and Convex (1955) and Waterfall (1961) were the main inspirations for up to three distinct optical illusions hidden within this algorithm. Expect Escher’s love of polyhedra – a few of which can be seen in Stars (1948) – to make appearances too!

-	_Arboreal._ This metaphor is illustrated as a tree with surrealist botanical components. It starts out, drawn on paper, as a root network from which a stem sprouts, branching into a fully developed crown with leaves, flowers, and/or fruit. Flowers are depicted as enlarged polyhedra with special properties, and fruit are cyclical structures inspired by the iconic Penrose triangle. Fruit can also, on occasion, be ripe with its own seeds, thus completing its life cycle. The pencil-to-3D effect is a reference to Reptiles (1943) and Drawing Hands (1948), except I take the metamorphosis to the present – becoming fully chromatic, dynamic, and interactive. The seed is planted in Escher's world, and blossoms into ours.

-	_Cryptographic._ Generative art is, in a way, the craft of making pseudo-random _art_ generators. Each output is the result of a cascade of calculations caused by one unique numerical seed, and in this case, it just happens to be an “Escherly” seed! For those curious about the details, I tried to avoid excessively obfuscating the code.

The viewer is encouraged to play with the artwork! In an effort to make the tree feel alive, I used an equation called the Kuramoto model which, most notably, mimics the flashing patterns observed in species of synchronous fireflies. Each cube is animated by an internal “clock” which is weakly coupled to its nearest neighbors. Interacting with these clocks will cause them to align, giving you the ability to synchronize or desynchronize certain areas of the tree.

Thank you to all who helped me along the way, no matter the weight of your contribution.

Special thanks: Jiahui Cai, Vincent Cohen, Daniel Bothner

Escherly Seeds

Lumina engages in the delicate interplay of curved, organic lines and abstract forms, weaving a surreal narrative filled with rhythm and dynamism. It illustrates dreamy imagery of cosmic phenomena such as electromagnetic waves, magnetic reconnection, and gravitational pull. In its composition, Lumina balances fluid and structured elements, vibrant and muted tones. The artwork’s glitchy and distorted textures, reminiscent of cosmic noise and stellar interference, further enhance its spatial narrative, offering a visual echo of the cosmic phenomena.

Lumina lies in its balanced integration of organic and digital elements. The first layer of the artwork, crafted with p5.js and a fBm shader, forms an organic texture, adding a swirl to give dynamism and generates diverse color palettes; establishing a visual field. This organic layer is then intertwined with a digital layer, where a custom fragment shader introduces subtle distortions and glitches, adding depth, complexity and luminance to the pieces. The inclusion of noise (and its artifacts) and various mathematical functions imbue the collection with a dreamlike ambiance.

**URL Parameters:**
?resolution=5000  :  to render as 2812x5000 px
?resolution=4000  :  to render as 2250x4000 px 
?resolution=3000  :  to render as 1687x3000 px (default)

**Press [S] in live view to save as .png**

This work involves intensive GPU processing. It's advisable to use modern hardware and ensure your browser's hardware acceleration is enabled for optimal performance. Using the Chrome browser on a desktop equipped with a high-end GPU is highly recommended.

See website for more details about the collection.

Lumina

**Blind Spots** is a series of abstract intimate portraits that distill human existence into two elements, the hidden essence of consciousness and the tangible shell of personality.

These elements are represented in the form of a glass sculpture. The first element within the sculpture, akin to a black hole, is a shape that defines itself through the surrounding characteristics it draws in. This halo of characteristics, like a beautifully radiant glass cover, symbolizes the constructed personality. Casting light on these black shapes, shielded by the identities they exhibit, the algorithm invites us to question our perceptions of those we encounter. How deeply do we truly know the people in our lives? It challenges us to consider if changing the perspective could alter our perception of them, while also offering the opportunity to simulate such a change with the help of animation. Perhaps the nature of our identities is as varied as the angles from which they are viewed?

Blind Spots serves as a depiction of my mental journey, transforming abstract thought patterns into a solidified artifact in the medium of generative art. The narrative is inspired by the diverse ways in which we perceive each other, a theme born from countless personal encounters. From a technical standpoint, it steps into uncharted territory for me, being the first artwork to emphasize high-resolution printing capabilities while maintaining real-time animation, a central element in my artwork. It is also my first on-chain project, prompting a restructure of the previous workflows.

Visually inspired by *Iittala - Kaleidoscope* exhibition, which displayed a mesmerizing interplay of glass sculptures and light, Blind Spots features a gradient backdrop punctuated by black shapes that undulate under the influence of a transmission shader, mimicking the iridescent shimmer of pearls. The geometry of the glass cover is crafted through the algorithmic movement of two curves revolving around each other. To produce high-resolution images suitable for printing, a bucket rendering technique with overscan was developed.

Articulated through two elements within each portrait, Blind Spots presents a visual metaphor for a human. This duality also echoes our presence on social media — carefully crafted showcases projecting a polished persona while concealing the authentic self. Together, the elements form a unique character from every point of view.

## Controls
- [ click ] - toggle animation
- [ s ] - save the current frame as an image

## URL parameters (see display notes)
- [ ?animate ] - animation on by default
- [ ?fill ] - responsive version to fill the browse
- [ ?width=x ] - render image with x width
- [ ?print ] - enable high-resolution mode (eg. ?print&width=10000)
- [ ?grainSamples=x ] - between 1 - 10
- [ ?refractSamples=x ] - between 1 - 5

Blind Spots

Drawing inspiration from the intricacies of nature and the physics theories that model it, "Fluiroso" (derived from "Fluidos Ruidosos") delves into the mesmerizing depths of Fluid Dynamics. This is achieved by implementing an accelerated solver for the Navier–Stokes partial differential equations.

Initial density and velocity are placed leveraging Perlin noise, and a selection of up to ten random velocity sources are positioned throughout the area. Augmented by other parameters such as boundary conditions and viscosity, the algorithm embarks on a dynamic journey tracing the solver's outputs over time. 

The resulting animation renders a delicate dance of brush strokes where the fluid becomes painter. The culmination is a repertoire of abstract pieces that evoke movement and invite viewers to discern emerging shapes and silhouettes.

Once the animation pauses to spotlight the artwork, viewers can engage with the piece and press 'p' to restart the movement. While many pieces continually evolve, others settle into a graceful equilibrium.

Fluiroso

Immaterial is a long form generative series exploring synthetic biology and botany through a combination of algorithms inspired by natural systems, such as recursion, growth, fluidity and fractal-noise. Originally influenced by the underlying structure of fungi gills, the series explores a wide range of formations and life forms, referencing possible futures where digital and organic systems merge. Through an interplay of 3D- and 2D-aesthetics, each iteration of the series generates a unique tapestry of shades and shapes aimed at creating space for interpretation, rather then directly mimicking the natural world.

Although each individual output of the algorithm ends up as an (almost) static composition, the motion leading up to this point is integral to the concept and experience of the artwork. Like in nature, simple rules define how the complexity of organic material unfold from a set of initial conditions. In this series the viewer is exposed to the process of how a seed grows into a fully fledged organism, revealing the underlying rule-based structure of both natural and digital systems.

_Immaterial is best displayed on vertically oriented screens. To ensure optimal performance, please view the artwork in a modern browser (preferably chrome) on a computer with a decent graphics card._

Keys
[space] - Pause animation
[s] - Download image
[w] - View wireframe

Immaterial

Spaghetti Bones is a celebration of my adaptation and exploration of the differential growth technique. The idea is simple. You start with a string of nodes connected to one another to form a shape. Each node feels 3 forces:
 - A repulsion force from all other nodes
 - An attraction force towards its immediate neighbors
 - An attraction force towards the midpoint between its neighbors

As you add more nodes into the shape, these 3 rules cause the shape to curve into itself, growing into a complex form of layered undulating lines. The goal is to create a shape that fills as much space as possible while maintaining a rigid form and avoiding overlapping itself. By focusing specifically on where and when you add more nodes, and how you interpret those nodes into a shape, there is much variety to be found in this simple algorithm.

Since I first learned about this technique, and wrote my own version based off these rules, I have been continuing to iterate, evolve, and optimize my code. It's an algorithm I always find myself coming back to, and has become my most researched topic and longest running experiment. I love its use of real life physics, and I find its outputs aesthetically pleasing on a deeper, almost instinctual level. 

Each output of 'Spaghetti Bones' starts with a simple shape as a seed for the differential growth algorithm. Throughout the rendering process, the shape is fed more nodes, and grows until it cannot find any empty space to fill. As it grows, a form is interpreted from the nodes of the growth and drawn onto the screen, creating a snapshot of the growth at that particular moment. There are many rules that govern how the shape grows, and how its form is interpreted, and these rules often evolve throughout the rendering process. When the render is complete, the resulting image is a full catalog of the history of the shape's life. 

The name of this project was created by Nicole, my girlfriend and an art wizard. Early on in the development of this project, I asked her to name an output I was sharing, and she chose to call it ‘Spaghetti Bones’ because that’s what it looked like. Since then, the name has stuck with me. I decided to keep the name for the final project in order to highlight the playfulness of each output, to encourage imagination when viewing this abstract art, and to thank Nicole for being tremendously supportive and helpful throughout my exploration of the art world.

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Spaghetti Bones #304

Joshua Bagley

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