### Welcome

Gregory B. Searle is a digital computer artist with a Bachelor in Fine Arts
from the University of Lowell (now U-Mass at Lowell) and a computer
programming background. He combined these seemingly opposing skill-sets
to create unique computer-generated “fractal” imagery using his own
custom computer code. This allows him to explore a whole world of
mathematically-generated imagery, carefully crafting the limitless
parameters to produce one-of-a-kind, high-quality fractal prints.
This page is intended as a space to explore computer-generated *fractal*
imagery as an art form.

At this time I am concentrating on extended variations of the
*Mandelbrot set*. In the future I may explore other types
of fractals. The extended set provides a huge world of form and
texture to explore. See the *About Fractals* page for more
information.

### Site Index

*About Fractals*provides more information on this medium.*Gallery*shows finished works that I have printed for sale.*Fractal Everywhere*is a link to the tool I built to explore and create.*Math & Art*goes into more detail on various subjects.*Resources*lists other pages of interest on this subject.*Wallpaper*is available for downloading for your phone or tablet.*Contact*me through the links on this page.

### New Artwork

There are multiple methods to depict a fractal rendering. “Flight” one uses *angular cycle counting*
to measure how rapidly each point changes. The result was unexpected. This is a fairly deep zoom into
the *Negabrot* (exponent of -2) using this technique. There is a lot of energy in this image.

An orderly progression of chromed surfaces resulting from a mild zoom into the multibrot set at a fractional
exponent below 2 with an Exponential function applied produces a fairly imposing image in “Order.” It is somewhat...
*Orwellian*... I attempt to title my pieces with words that reflect not only what appears to be
there, but how they *feel*.

### New Fractal - Newton

*Newton*

The *Newton* fractal illustrates the chaotic nature of the *Newton method* for iteratively
discovering the roots of a complex equation. By default, it renders in the Julia set, but things get interesting using
other rendering options. This fractal is essentially a Multibrot formula divided by its derivative.
Try it out: Fractal Everywhere

### Trigonometric Variants

New functionality in my *Fractal Everywhere* software allows trigonometric
functions to be injected into the Multibrot formula. “Synergy” is a slice
through Multibrot space with sine and tangent functions applied. The greyscale scheme
allows the subtle shading and forms to take precedence.

### Julia Set

*Julia of Mandelbrot Cubed*

The *Julia Set* renders Mandelbrot variants a little differently.
Using a reference point in the set, it renders against this point to produce a fairly
regular, symmetrical fractal shape. It's not quite as complex as the base set, but
can produce some beautiful imagery. Fractal Everywhere
now supports Julias. Click on “Julia” next to the formula menu to render
the Julia for the currently displayed coordinates. This acts as a toggle, so you can
switch back-and-forth. It's available for all fractals.

### New Fractal - Tower of Powers

*Tower of Powers*

*Multibrot at 1,000 Expoent*

*Tower of Powers* calculates the initial value *c*
raised to the power of the result *z* over and over again, *z = c ^{z}*,
starting with

*z = 1*. You would think that this would quickly escape to infinity, but there are some stable areas that produce interesting results. This is very similar to what appears when you render the Multibrot with a very high exponent. For more information see Cleve Moler's article on the subject. Check it out in my Fractal Everywhere.

### Fractal Wallpaper

Download fractal wallpaper for your phone, tablet, or other device
free from my Wallpaper page!
*Fear of the Dark* comes from the fragmented space in the negative exponents around -1.5.
Dark and mysterious, it has a lot of interesting things going on in the details. Check out the page for more.

### “Special Merit” and “Special Recognition”

*Clematis* received Special Merit and *Equinox* received Special Recognition in the the March 2018 Light Space & Time
Online Art Gallery's 9th Annual Abstracts Art Exhibition. Following are a couple of excerpts from
the gallery:

“The gallery received 952 entries from 29 different countries from around the world. In addition, the gallery received entries from 40 different states.”

“The gallery also included Special Merit awards and Special Recognition awards for outstanding art. Many of the artists in either of these groups could have easily been included in the upper tier of our winners, as their art was also exceptional.”