I have some quaternion functions, like ln and exp. If I want to go to 5-component numbers, I can easily migrate the ln and exp functions by adding in an extra imaginary component. Since 5-component numbers do not have a multiplication operator defined, why not just do exp(ln(Q1) + ln(Q2)) instead of the missing Q1*Q2 functionality?
I tried it out with the quaternion Julia set, and it sort of works. Attached is a figure of the standard Julia set, Z = Z^2 + C.
Why is there no multiplication operator in 5D anyway?
The exp function is:
float mag_vector = std::sqrt(qA->y * qA->y + qA->z * qA->z + qA->w * qA->w);
temp_a_x = qA->x;
qOut->x = std::exp(temp_a_x) * std::cos(mag_vector);
qOut->y = std::exp(temp_a_x) * std::sin(mag_vector) * qA->y / mag_vector;
qOut->z = std::exp(temp_a_x) * std::sin(mag_vector) * qA->z / mag_vector;
qOut->w = std::exp(temp_a_x) * std::sin(mag_vector) * qA->w / mag_vector;
To add in a 5th-component, one would have to just alter mag_vector to include it, and then change qA->whatever to qA->a where a is the 5th component.