Fermat’s Spiral

Fermat’s Spiral — featured in our Signature collection — transforms a simple mathematical principle into a composition of balance, growth, and natural symmetry. This print traces two intertwined spiral branches, each winding around the centre in perfect opposition and completing twenty full rotations. The construction ensures every turn is spaced evenly, evoking forms seen in nature from sunflower heads to galaxy arms.

Mathematically, the distance from the centre increases in direct proportion to the angle swept around — resulting in a spiral where each arm unwraps at a constant rate. One branch is plotted forwards, starting at zero degrees, while the other is mirrored across the centre by beginning at one hundred eighty degrees. Both are scaled so their tightly woven arcs meet a fixed outer radius. Coordinates for the spiral branches are found by multiplying the scaling factor, the square root of the swept angle, and then using both the cosine and sine of that angle to assign every point’s horizontal and vertical placement.

The remarkable aspect of Fermat’s spiral is how it encodes optimal packing and distribution. In botany, similar spirals allow seeds or leaves to fill space efficiently, while in mathematics, the same pattern surfaces in areas from polar graphing to visualisations of irrational numbers. The layout ensures no two points overlap — demonstrating an arrangement that is as logical as it is aesthetically pleasing.

Each museum-quality print is rendered in crisp detail on 250gsm archival matte paper. The smooth, durable finish beautifully complements the sweeping, precise lines of the spiral, offering a timeless and contemplative celebration of mathematical artistry.

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.

Full delivery information →

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 →