Here are some images from a calculation I did a while back. It is blurry because my gpu only supports floating points. I am not sure how to prove infinite area, or how to find fractal dimension. Many seem to look like Mandelbrot Set images, but this one looks a bit different.

Full Set like the Mandelbrot Set (11.4 MB gif)

Sub Set like the Julia Set (22.3 MB gif)

Full Set zoomed out to show infinite area (9.8 MB gif)