#threadedtheorems

[threadedtheorems]

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

[threadedtheorems]

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.

[threadedtheorems]

Close-up of the chaos! These swirling stitches follow the Lorenz system’s rules. Even the tiniest change in starting point decides how many times we loop each lobe. One stitch to the left? Whole new journey

[Free embroidery pattern]

[threadedtheorems]

This embroidery traces the streamlines of slow, sticky flow—what mathematicians call Stokes flow. ✨

In this regime, everything moves smoothly and predictably, like a billiard ball sinking into syrup. The closer the lines, the faster the flow. Far away, the sphere’s influence fades, and the lines stretch out to be uniform. [Free embroidery template]

[threadedtheorems]

Each curve in this embroidery traces the path of slow moving fluid around a sphere—stitched by hand, shaped by maths.

[Free embroidery pattern]

[threadedtheorems]

This embroidery captures a fragment of the Penrose tiling, a mathematical marvel where two simple shapes—a kite and a dart—come together to form a pattern that never repeats.

Unlike checkerboards or honeycombs, this tiling is aperiodic: every little motif (like this star) pops up infinitely often, but there’s no way to slide the whole thing and make it match itself.

This section is from the P2 tiling, one of several discovered by Roger Penrose in the 1970s.

[Free embroidery pattern]