Hybrid fractals occur when you alternate between fractal formulas during the inside iteration loop of generating a fractal. The idea came from posts on the old Fractal Forums site.
For example, rather than the usual Mandelbrot Fractal iteration, you can modify the inside loop to alternate between the Mandelbrot, then the Burning Ship, then the Mandelbrot, and the Mandelbrot again. You then repeat the sequence for as many iterations as that pixel needs.
This gives a result like the following
The code to create this (and other hybrid formulas) is included with Visions of Chaos, but you can also see the OpenGL shader code for it here.
I have also used the same hybrid technique for 3D Mandelbulb Fractals as shown here.
The Burning Ship Fractal is a slight variant on the Mandelbrot Set Fractal.
The basic Mandelbrot Fractal formula is z=z^2+c. The Burning Ship Fractal formula is z=abs(z)^2+c.
The following image is the standard power 2 Burning Ship Fractal rendered using CPM smooth coloring.
Zooming in to the right antenna part of the fractal shows why it was named the Burning Ship.
The next 3 images change the exponent 2 in z=abs(z)^2+c to 3, 4 and 5.
The same power 2 through power 5 Burning Ships but this time using Triangle Inequality Average (TIA) coloring
The next 4K resolution movie shows a series of zooms into Burning Ship Fractals between power 2 and power 5 colored using CPM coloring
and finally another 4K movie showing more Burning Ship zooms colored using TIA coloring
All of the above images and movies were created with Visions of Chaos.