Strings

DGIFS11e, an example of mathematical art, a fractal made with a 3-vertex directed graph IFS.

Here is a fine art print of this picture.

For this picture the (complex) functions assigned to the edges of the directed graph are inverse branches of quadratic polynomials associated with connected Julia sets. That is the inverse branches f_c,1⁻¹(w) = + (w − c)^1/2 and f_c,2⁻¹(w) = − (w − c)^1/2 of f_c(z) = z² + c where c is inside the Mandelbrot set. Other pictures created using the same functions are Static 1, Static 2, Static 3 and DGIFS11a.

A fractal animation “Circular Strings” (4m) which uses this image is on YouTube, where there's a 1080p version and a 4K version. The guitar instrumental “Circular Strings” is the soundtrack and is available on some music streaming services.