This correction is way too long in coming, I hope it didn't mess anyone up. I have been corresponding with Wes Loewer, Fractint's arbitrary precision author. He is teaching math and physics in Nairobi, Kenya at Rosslyn Academy (http://www.rosslynacademy.com) which is an American curriculum K-12 school. We passed along this correction, which I have verified. In any case, it turns out that the formula for the quaternion product in both the Fractint docs and Fractal Creations 2nd Edition is wrong. The current (wrong) formula for quaternion (x,y,z,w) is: q1q2 = 1(x1x2 - y1y2 - z1z2 - w1w2) + i(y1x2 + x1y2 + w1z2 - z1w2) + j(z1x2 - w1y2 + x1z2 + y1w2) + k(w1x2 + z1y2 - y1z2 + x1w2) The correct formula is: Then q1q2 = 1(x1x2 - y1y2 - z1z2 - w1w2) + i(y1x2 + x1y2 - w1z2 + z1w2) + j(z1x2 + w1y2 + x1z2 - y1w2) + k(w1x2 - z1y2 + y1z2 + x1w2) Fortunately, this multiplication function isn't coded up in fractint anywhere, and as far as I know, none of the quaternion fractals is wrong. (At this point if they WERE wrong I'd leave them as is for backwards compatibility.) Also fortunately, the hypercomplex formulas in the documentation and in the code appear to be right. Clyde Davenport's book on hypercomplex numbers is now online. This was my main source on hypercomplex numbers. The link is: http://home.usit.net/~cmdaven/cmdaven1.htm A useful link that includes formulations of some analytic functions of the quaternions that would probably be suitable for fractal implementations (maybe even in fractint) is: http://world.std.com/~sweetser/quaternions/intro/tools/tools.html Tim