# Alessandra Fleck – Looking Outwards – 05

For this looking outwards I wanted to explore a project that I find particularly interesting by former Apple programmer Ben Haller called Attraction Basins. Each of the different art pieces created in this project are made using a form of “equation root finding.” The pieces in this project are very much related to the Mandelbrot Set and the idea of points on a place relating to points on an image, to which the root-finding is utilized iteratively.

The first image below titled “Carapace” was generated using  Newton’s Method, which has to do with the idea of finding roots based on a process of successive approximations.

(The image above showing “Carapace” by Ben Haller)

The colors that occur in the pieces are dependent on the length of time and type of root that was converged. At these points of convergence also note the “basins” that occur in these areas. The other piece from Ben Haller’s gallery I wanted to look at is called “Energy.”

(The image above shows “Energy” by Ben Haller)

This piece is based on the Secant Method which is another root finding algorithm that takes a “region of interest” and assumes a linear relationship of the function  being analyzed. A graph of how the secant method works can be seen below. Note the relationship between the graph and the art piece generated from it.

I find these 3D Computer Graphics interesting because they relate directly to some form of root finding. So as diverse as the two might read in visual language, there is a common underlying method that carries across all the pieces.

http://www.sticksoftware.com/gallery/basins.html

http://mathworld.wolfram.com/SecantMethod.html

https://en.wikipedia.org/wiki/Newton%27s_method