Signature series
Apollonian Gasket
Fractal geometry · Circle packing · c. 200 BCE
- Original infographic and mathematical visualisations by Simon Tyler
- Featured in The Guardian · The Times · Elle Decoration
- Free UK delivery on every order · Worldwide shipping
Named after Apollonius of Perga, who first studied tangent circles around 200 BCE. Starting with four mutually tangent circles, the Apollonian Gasket fills every remaining gap with smaller and smaller circles, infinitely. A fractal that predates the concept of fractals by two thousand years.
About this print
About this print
Start with four circles, each touching the other three. In every curved gap between them, draw the largest circle that fits. Now there are more gaps, and each of those takes another circle. Repeat forever and the result is an Apollonian gasket: a surface of circles that never overlap, never quite fill the plane, and shrink towards infinity.
The curvatures behave remarkably. Descartes showed in 1643 that any four mutually tangent circles satisfy a fixed relationship between their curvatures - and a consequence is that if the first four are whole numbers, every circle in the gasket that follows is too, all the way down. The picture is geometry; the numbers underneath it are pure arithmetic.
Apollonius of Perga was working on tangent circles around 200 BCE, some two thousand years before the word fractal existed. The gasket has a Hausdorff dimension of about 1.3057: more than a line, less than a surface, which is a precise way of saying it sits between dimensions.
Part of the Signature series of mathematical art prints.
The Signature series
The Signature series
Signature is a collection of mathematical, scientific and infographic visualisations - prime number distributions, evolutionary trees, geological timescales, and other structures that become something unexpected when rendered at print scale.
Each piece begins as a data-driven computational process and is developed into a finished artwork through a combination of custom code and design refinement. The aim is not to illustrate mathematics but to make the underlying structures visible - to find the image that was always inside the data.
The series draws on fields including number theory, evolutionary biology, palaeontology, topology, and information design.
Paper and printing
Paper and printing
All prints are produced to order on 250gsm archival matte paper using pigment-based inks, chosen for colour accuracy and long-term stability.
Each print is rolled in acid-free tissue and shipped in a rigid cardboard tube, sealed for moisture protection, ready for framing on arrival.
Dimensions
Dimensions
Large · 50 × 70 cm · 20 × 28 in
XLarge · 70 × 100 cm · 28 × 40 in
Delivery
Delivery
UK: Free · 3-5 working days
Europe: €8.50 · 3-7 working days · No customs charges
USA & Canada: $8.95 / $12.00 CAD · 5-10 working days
Australia: $14.00 AUD · 5-10 working days
Rest of World: £14.95 · 7-14 working days
All prints are produced to order and dispatched within 1-3 working days. Orders placed before 5pm GMT ship the same day. You'll receive tracking information by email once dispatched.
Orders outside Europe may be subject to local customs charges on delivery - these are the responsibility of the recipient.
Returns
Returns
Returns accepted within 30 days. Email returns@axisophy.com with your order number and we'll provide return instructions.
Return postage is the customer's responsibility except where the print arrives damaged or there's been an error - in which case we'll arrange a replacement or refund immediately, no return needed.