The Artist's Husband: Svensson Attractors


Ash nazg durbatulûk, ash nazg gimbatul, ash nazg thrakatulûk agh burzum-ishi krimpatul.

One ring to rule them all, one ring to find them, one ring to bring them all and in the darkness bind them.

— J. R. R. Tolkien’s The Lord of the Rings (1954–55)

I’ve been going on and on about de Jong attractors lately , but that is only one kind of attractor. There are many others! This image is a Svensson attractor. It uses a set of equations very similar to what the de Jong attractor uses, and also requires four constants which define the shape of the result. Because of the way it handles sine and cosine, circular results are far more common than with the de Jong equations.

The Svensson equations look like this:

$$ x_{t+1} = d * sin(a * x_t) - sin(b * y_t) $$ $$ y_{t+1} = c * cos(a * x_t) + cos(b * y_t) $$

The constants for this post’s image are:

Constant Value
a 1.2
b -1.56
c 1.8
d 7