Quaternions are a 4-dimensional extension of complex numbers, represented as x + iy + jz + kw where x,y,z,w are real numbers, using the components i,j,k defined by i² = j² = k² = ijk = -1. The Mandelbrot set equation Z = Z² + C works the same when quaternions are used, and the Mandelbrot set remains unchanged for points in the complex plane, w + ix. However, it extends the fractal into 4D. The viewer draws a 3D slice of x,y,z, using a constant w set by the "Slice W" slider. Use the clipping plane to see the Mandelbrot set on the xy plane in the cross section where z=0. Since quaternions are not commutative, rotations produce interesting effects when added at each iteration of the Mandelbrot formula. The XZ, YZ, and XW axes are the most unique due to symmetry with the other three. Use Julia mode to draw the Julia set at a specific point. Drag the point to adjust it, or enter coordinates. The w coordinate must be specified manually. Use the precision value to specify the size of the smallest details to resolve. The "Fast Controls" option temporarily lowers the resolution when you adjust the view so that it responds smoothly.
With a mouse, click and drag to rotate the view. Hold the Shift key to pan. Hold the Alt key or use the scroll wheel to zoom.
With a touchscreen, move one finger to rotate the view, and two fingers to pan. Pinch to zoom.