Modular Circles MC0002

Mark a number of points evenly around a circle and label them 0, 1, 2, and so on. From each point, draw a straight line to the point with twice its number, wrapping around when the count exceeds the total. That is the entire construction: no curves are drawn, only straight lines between marked points.

A cardioid appears. Not an approximation of one - the envelope of those straight lines is exactly the heart-shaped curve that forms in the reflected light inside a coffee cup, and which bounds the main body of the Mandelbrot set. Nothing in the instructions suggests a curve should emerge at all.

The rule generalises. A multiplier of three produces a nephroid with two cusps, four produces three, and so on: the number of cusps is always one less than the multiplier. Each is an epicycloid, the curve traced by a point on a circle rolling around another circle, arrived at here by a route that involves no rolling and no circles beyond the first.

The construction is old enough to have been a schoolroom exercise with pins and thread, and simple enough to explain in a sentence. What it demonstrates is that curvature can be an emergent property of straight lines - that a shape can be present in a rule without being present in any of its parts.

Part of the Signature series of mathematical art prints.

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 · 70 × 70 cm · 28 × 28 in

XLarge · 100 × 100 cm · 40 × 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.

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