Platonics

A response to being buffeted by forces outside of our control. Platonics sought to find order, control and solace in the Platonic solids. Instead it found beauty and intrigue in the emergent chaos that can arise from even the simplest systems.

Its building blocks are the five Platonic solids. Forms which have fascinated humanity for thousands of years. Their title comes from the philosophy of Plato, who equated each of the solids with a classical element.

Platonics arranges these forms in a series of geometric layouts, with varying density and randomness. At one extreme we see tidy radial circles consisting of a single solid. At the other, packed pentagons consisting of jumbled solids give rise to Escher-esque compositions which hold near infinite variety, variety enhanced by a range of pens and colours that draw and fill those solids.

This relationship between order and disorder is at the heart of Platonics. The collection seeks to show how they are not so far removed from one another – and how we might embrace them both. It also aims to give collectors a behind the scenes look at how generative compositions can be constructed.

The geometric proof that there are only five convex regular polyhedra (the Platonic solids) states that at each vertex of the solid the angles between adjacent sides must be less than 360 degrees. This amount less than 360 degrees is known as the defect angle. It is from this geometric proof that the pricing for Platonics is derived – a Dutch auction priced according to the defect angles of the five Platonic solids: 180 > 120 > 90 > 60 > 36.

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The Solids

A Platonic solid is a convex regular polyhedron, of which there are only five. For Plato, each represented a classical element: the tetrahedron represented fire, the cube earth, the octahedron air, the dodecahedron the ether and the icosahedron water.

These five solids have remained of interest in the millennia since Plato’s characterisation. In the 16th century Kepler sought to use them in his model of the solar system. In more recent times, the Platonic solids have been important building blocks in computational art and graphics.

From Order to Disorder

Platonics began life as a very structured algorithm – finding solace in order amidst the swirling chaos and uncertainty of early Winter. But that soon changed.

One of the joys of the generative method is the sense of collaboration with the algorithm. Though you created it, you don’t really know what it is capable of until you’ve pushed and pulled it in various directions. Inevitably, one of those directions proves particularly fruitful and provides a new focus.

In the case of Platonics, increasing the density of the solids – allowing them to overlap rather than forcing them apart – produced a fascinating range of compositions . The underlying forms became increasingly abstracted. Despite knowing exactly how they were composed it became very hard to deconstruct them visually, an exciting demonstration of emergent complexity.

Behind the Scenes

With this collection we want to take the collector behind the scenes and demonstrate how a handful of simple forms and rules can give rise to a striking range of compositions.

To that end, we have animated the rendering of each Platonics such that each solid is drawn one by one.

This approach highlights how complex, chaotic compositions can arise from fairly straightforward initial conditions.

It also makes for rather soothing and hypnotic viewing, ensuring that the rendering of each piece is as much a part of the experience of the artwork as the final image.

We've spent hours and hours watching these render so can only hope they prove as captivating for you.

Behind the Scenes

With this collection, we want to take collectors behind the scenes to demonstrate how a range of compositions can be constructed from a simple set of forms and rules. To that end, we have animated Platonics such that each solid is drawn one by one – making the rendering of each piece as much a part of the experience of the artwork as the final image. Scroll to the top to see this rendering in action. We hope you find it as hypnotic as we have.

Layouts

The Platonics algorithm takes a highly structured approach to layout. The solids are laid out according to one of four different shapes. The triangle, square and pentagon layouts callback to the polygons from which the Platonic solids are composed. The circular layout provides a smooth contrast.

Layouts are either spaced, with room left to breathe between the concentric rings of solids, or packed, with the solids overlaid on top of each other. It is fascinating how changing this one variable gives compositions a completely different feeling.

Subtler variation comes from the order solids are drawn on the page. They can be drawn from the outside inwards or the inside out. They can be drawn clockwise or anticlockwise.

Different mints consist of a different mix of solids. Often, just a single solid is used. Sometimes the solids change per concentric ring or per side. Other times they are selected at random throughout the entire composition. These mixes help the collection span simple harmony to glorious chaos.

In continuing to interrogate the balance between order and disorder, Platonics can be constrained or unconstrained. When constrained, contrasting or complementary borders help frame the mint. When unconstrained, the solids are set free to cover the entire canvas.

Colour & Texture

Platonics aspires to be a playful, colourful collection. To invoke that playfulness, we utilise the four different pen types that were initially developed for Paper Planes: Ink, Pencil, Gel and Dip.

Colours are applied according to four possible fill types. Each solid can take on a single colour. Each face on the solid can be a random colour selected from the palette or a fixed colour from the palette. Occasionally just the outline of the solids will be drawn, accentuating their forms.

There are 20 different colour palettes, in harmony with the maximum number of faces a Platonic solid can consist of. The palettes skew towards the colourful, albeit with some more muted or monochrome.

Some of those palettes draw on previous collections, others were created anew. The palettes are: Galah, Rock Thrush, Fairywren, Blackbird, Kingfisher, Golden Pheasant, Lilac Roller, Swallow, Flameback, Jacaranda, Apricot, Nightcall, Marooned, VHS, Sideshow, Horizon, Pipe, Spectrum, Liqourice and Rose.