#threadedtheorems

This full binary tree branches out over 8 levels 🌿✨, stitched with stem stitch and dotted with French knot leaves. Who knew recursion could look so cute? Template in my blog description if you want to stitch your own!

Work in progress of a binary tree.

The Koch snowflake is a fractal made by repeatedly adding smaller triangles to the middle of each edge of an equilateral triangle. Every iteration, each edge turns into four edges that are a third as long, which makes the perimeter grow by a factor of 4/3. Keep repeating this forever and the perimeter becomes infinite! But, even though you keep adding more and more tiny triangles, the extra area you add each iteration gets smaller and smaller. This means the total area settles down and approaches a finite value - 1.6 times the area of the original triangle. So the Koch snowflake has an infinite perimeter and a finite area!

This embroidery recreates the first published image of the Mandelbrot set from 1978, using thread to capture its striking symmetry and spiky outline. The Mandelbrot set is a famous fractal formed by repeatedly applying an iterative equation​ to the complex numbers. Each complex number can be represented as a point on a 2D plane. If the results of the iterative equation starting at a specific point stay bounded, the point is in the Mandelbrot set. Points outside the set are generally coloured based on how fast they escape, forming the fiery fringes around the edge.

[free embroidery template]

Sneak peek of a new maths embroidery design 🤠

The Lorenz system describes how a point’s position in 3D space changes over time, showing chaotic behaviour. The resulting path forms butterfly-shaped lobes. Small changes in the starting point lead to vastly different trajectories around the lobes. This concept is linked to the "butterfly effect" in chaos theory. Free embroidery pattern

Penrose tiling embroidery in front of the Penrose tiling at the Oxford Mathematical Institute