Abstract
In this article we extend Lambert's W function in the space of quaternions, calculate the norm of the quaternion W function, and derive formulas for the left and right quaternion derivatives for f(z)=cz . We also examine the contractivity for the iterates of f in the space of quaternions with the help of the quaternion W function, and generalize the results on the convergence of the complex iterated exponential zz … z in the space of quaternions. Finally, we present 3D representations of the convergence subspace for the iterated exponential and of several Julia sets in the quaternion space generated by a quaternion fractal program.
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