Evolutionary computation to search Mandelbrot sets for aesthetic images

Figures & data

Figure 1. The quadratic Mandelbrot set together with nearby regions of the complex plane (left) and an enlargement of its upper-right flank (right).

Figure 2. A view of the cubic Mandelbrot set and the surrounding areas of the complex plane.

Table 1. Desired divergence values for the first mask, the mask derived from equation (1)

34	40	47	53	58	60	58	53	47	40	34
40	49	60	70	78	82	78	70	59	49	40
47	60	75	93	109	115	109	93	75	60	47
53	70	93	122	150	162	150	122	93	70	53
58	78	109	150	193	200	193	150	109	78	58
60	82	115	162	200	200	200	162	115	82	60
58	78	109	150	193	200	193	150	109	78	58
53	70	93	122	150	162	150	122	93	70	53
47	59	75	93	109	115	109	93	75	59	47
40	49	60	70	78	82	78	70	59	49	40
34	40	47	53	58	60	58	53	47	40	34

Figure 3. A spiral view and a starburst view selected from the quadratic Mandelbrot set. These views are used to generate induced masks.

Figure 4. The 20 best-of-run views of the quadratic Mandelbrot set (upper) and the cubic Mandelbrot set (lower) found using a fitness function incorporating the first designed mask.

Figure 5. The 20 best-of-run views of the quadratic Mandelbrot set found using a fitness function incorporating the second designed mask. See insert for colour version of this figure.

Figure 6. The 19 best-of-run views of the quadratic Mandelbrot set using a fitness function derived from the spiral view. The spiral is displayed as the first image. The upper set of images uses a 21 × 21 grid while the lower uses 31 × 31.

Figure 7. The 19 best-of-run views of the quadratic Mandelbrot set found using a fitness function derived from the starburst image. The starburst itself is displayed as the first image in the set. These images use a 31 × 31 sample grid.

Figure 8. Squares in inverted grey scale above show the locations of views found by the evolutionary algorithm using the first mask on the quadratic Mandelbrot set. The squares shown above are substantially larger than the actual views; all views are smaller than single pixels at this scale.

Figure 9. A view located with an alternate fitness function that failed to find a diversity of visual characteristics.