Mandelbrot Set Mountain, 3D Printed Fractal Relief with Its Equation Engraved Underneath

The Mandelbrot set as a landscape. Each point c of the plane is raised by how many steps z → z² + c takes to escape. The points that never escape form the flat summit, which is the set itself; the cliffs and ridges around it are the edge of the fractal. Under the base we engraved the rule that draws it: z₍ₙ₊₁₎ = zₙ² + c, starting from z₀ = 0, and c belongs to the set when |zₙ| ≤ 2 for every n. Colour that follows the height: the piece is printed layer by layer from a gradient filament, so each height gets its own band of colour, much like computer images of the set are coloured by escape time. Where each colour lands depends on the spool, so no two pieces are the same. Two filaments: • Silk rainbow: shiny, runs through the rainbow from base to summit. • Matte sunset: orange into pink, with a soft matte finish. • 11.2 × 8.4 cm, 2.8 cm tall (4.4 × 3.3 × 1.1 in), about 75 g • PLA, printed layer by layer; the layer lines trace contour lines, like a topographic map • Designed by us and printed to order by our production partner Slant 3D in the USA • Decorative only: not a toy, not for food, keep away from heat above 50 °C (120 °F) The photos are digital renders made from the real print file. The colours shown are a simulation; the real bands vary from piece to piece. Shipping to the United States is included. We also ship to Canada, the United Kingdom, Ireland, Germany, France, Spain, the Netherlands, Australia, New Zealand, Japan, Mexico and Chile for a flat 14.99 USD, shown at checkout before you pay.