Fun visualizations with quaternions.
In this project, I plot a vector of quaternions on a two dimensional grid. The X axis reperesents the element in the quaternion vector. The Y axis represents the versor value of the real component of each quaternion. For the red, green, and blue values of each pixel, I used the values of the imaginary components of the versors. for instance, the unit quaternion would be gray (255/2 for each imaginary component). Negative values go to 0, positive values go to 255.
Adding complex components
In the picture below, I started with the quaternion -1 - 1k, and added 0.02i for every element in the size 400 quaternion vector.
Rotating a quaternion
This one is more interesting - I am rotating the -1 + 0.5k quaternion by the 0.999550 + 0.029987i quaternion. Notice that the rotation quaternion is a versor (it has a norm of 1). Since it’s nearly entirely a real versor, it rotates slowly around both the real and complex components, which is why the below image is sinusoidal in the Y axis and in color space (it rotates through colours) !