## Mandelbrot/Julia hybrids

Consider the Mandelbrot and Julia formulas:

z_{n+1}=z_{n}^{2} + c_{m}

z_{n+1}=z_{n}^{2} + c_{j}

Where c_{m} is changed for each pixel when calculating the Mandelbrot image and c_{j} is constant for each pixel when calculating Julia images.

The hybrids below uses different methods to mix the two c's together in one picture.

Part 1

Alternates between using c_{m} and c_{j} using different patterns for each iteration.

Part 2

c = (1 - k) * c_{m} + k * c_{j}, With k = 0 at iteration 1 and k = 1 at maximum iteration.

Part 3

c = (1 - k) * c_{m} + k * c_{j}, With k = 0.5 * sin(period * iteration) + 0.5.

Several different periods were used.

Part 4

c = 0.5 * c_{m} + 0.5 * c_{j}