Apollonian Gasket

This Apollonian Gasket print presents a classic fractal geometry in striking, precise form. This print begins with a configuration of four starting circles, defined by the root quadruple curvatures: negative twelve, twenty-five, twenty-five, and twenty-eight. Through seven intricate rounds of replacements, new circles are recursively added to fill every possible gap, building up an intricately layered structure.

Each step multiplies the pattern, with circles added in quantities like three, nine, twenty-seven, eighty-one, and eventually over two thousand per depth. The increasing totals quickly soar, culminating in thousands of finely nested shapes.

This geometric marvel is rooted in mathematical history and named after Apollonius of Perga, who first studied problems related to tangent circles in ancient Greece. The Apollonian gasket exemplifies how simple rules — here, the replacement of gaps with smaller, tangent circles — can yield endlessly complex, self-similar forms. Its one-axis mirror symmetry (classified as D₁) and a universal Hausdorff dimension of roughly 1.30568 make it a showcase for both symmetry and fractal dimension in mathematics.

The recursive process not only reveals the interplay of geometry and number, but also connects to deeper questions about packing, symmetry, and the distribution of curvatures. Each layer exposes a greater depth and an unexpected richness — visual proof of how mathematical abstraction finds order within limitless complexity.

Every print is produced in open edition on museum-grade 250gsm archival matte paper, lending both weight and subtlety to the fine detail. Crisp contrasts and a soft matte finish highlight the minute geometry, resulting in a timeless and contemplative addition to any collection or space.

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.

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.

Large · 50 × 70 cm · 20 × 28 in

XLarge · 70 × 100 cm · 28 × 40 in

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.

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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.

Full returns policy →