Here is a comparison of generating models using a search for an edge versus a fixed grid. Both models are constructed using the same fractal resolution.
Halley Model using search, portion of 640 x 480
Halley Model using grid, portion of 640 x 480
comp1_high.jpg
comp1_grid.jpg
Mandelbrot using search at 80 x 80
Mandelbrot using grid at 80 x 80
comp2_high.jpg
comp2_grid.jpg