# Regina Valluzzi

Dr. Regina Valluzzi explores abstract mathematical and scientific concepts through complex geometric paintings. Many of the subjects of her abstract drawings and paintings are taken from topics in mathematical and theoretical physics, and focus on the mathematical tools that find application in the physical sciences. Soft Matter Physics and Biological Physics ideas are often seen, arising from Dr. Valluzzi's main area of research for many years. In addition to motifs and ideas drawn directly from molecular biology, biophysics, and nearby fields, her art often incorporates aspects of "fractal" order. Rather than the well-popularized geometric fractals used in digital image creation, she focuses on "fractal" as a general mathematical idea, indicating self-similarity. There are fractal or self-similar elements in the way the color, shape and thick and thin line geometries relate, their local arrangements, and the way they coordinate to fill and texture a defined volume.

Green functions are a special type of integral. In calculus, integrals provide methods for adding up functions and trends. Everyday single integrals work in 2 dimensions. A function creates a curve on the plane and solving its integral tells you how much total area the function covers.

Green functions and path integrals can be very useful for examining functions that exist in fields - where instead of an empty paper or box, each piece of the space holding the function has values associated with it (electric field strength, color, temperatu

A somewhat abstracted and fanciful painting of a vector field. There is, to my knowledge, no non-abstracted way to paint a vector field. This particular vector field features patterns from liquid crystal physics, along with the general div, grad and curl + cross and dot product definitions, and the non-chiral terms of the Frank elastic free energy for liquid crystals (twist, splay, and bend deformation contributions). The first thing the hubs said when he saw it was "ooooh, nabla!"

A scalar field is simply a space with a quantity assigned to each point. Each set of coordinates pulls up a value for the field in addition to a location in the space. A vector field is populated with vectors. Each set of coordinates pulls up a vector magnitude and direction. Many of the features of nematic liquid crystals are described in terms of where the molecule (or optical or dipolar) axes point on average, how uniformly they point, and how the pointing direction varies in a liquid or solidi