We present an approach to describe the fusion of two heavy ions in which the colliding system has access to a wide spectrum of shapes through the utilization of an auxiliary reference frame and the employment of a multipole expansion of the nuclear radius with the dipole term treated as an actual and leading shape variable. Access to fusion shapes that would otherwise be unattainable is possible by initially placing the origin of the auxiliary reference frame in the neck region between the colliding nuclei. The fusion process is modeled as an unconstrained biased random walk in a four-dimensional deformation space with step probabilities correlated to the density of available states. Deformation energy is calculated using the macroscopic-microscopic method, incorporating rotational energy. The presented approach successfully describes fusion probabilities for reactions involving ${}^{48}\mathrm{Ca}, {}^{50}\mathrm{Ti}$, and ${}^{54}\mathrm{Cr}$ projectiles with a ${}^{208}\mathrm{Pb}$ target.

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• Fission
• Level densities
• Nuclear fusion
• Nuclear reactions
• Nuclear shapes and moments
• Synthesis of new superheavy elements
• Metropolis algorithm