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We present a model of two-kinks resulting from an explicit composition of twostandards kinks of the $\phi^4$ model based on the procedure of Ref.\cite{uchiyama}. The two-kinks have an additional parameter accounting for theseparation of the standard kinks of $\phi^4$ model. We have shown that thetwo-kinks have two discrete internal modes besides the zeroth mode and thecontinuous spectrum. This new feature signalizes that the head-on collision atwo-kinks/two-antikinks pair exhibits a rich and complex behavior due to theadditional channel from which the energy of the system can be stored. We haveexhibited the fractal structure associated with the main configurations afterthe collision. We have inferred the fractality as the imprint of the nonlinearexchange of energy into the two discrete internal modes.

A note about a new class of two-kinks