Gregg Helt

Healdsburg, California, USA
I find beauty in the way that relatively simple mathematical equations can give rise to complexity, and I render this complexity as images. My art in this exhibition uses techniques from my paper "Extending Mandelbox Fractals with Shape Inversion". The Mandelbox is a class of escape-time fractals that use a conditional combination of reflection, spherical inversion, scaling, and translation to transform a point under iteration. By using a more generalized type of shape inversion instead of spherical inversion, I can explore new types of Mandelboxen fractals in my art.
HyperMandala #1
60 x 60 cm
digital print on aluminum
The standard Mandelbox transform can be applied to points in any n-dimensional Euclidean space, and the same applies to shape inversion Mandelboxen as long as n-dimensional shapes are used. This piece is a 3D slice through a 4D Mandelboxen that uses a shape that is a linear blend of a 4D hypersphere (glome) and a 4D hypercube (tesseract) for the shape inversion. Shading of points which don't escape is determined by a combination of closest approach under orbit to the coordinate axes and the origin.