In this study, the effect of multiscale geometry on the near-field structure of an axisymmetric turbulent jet is examined at a global Reynolds number of ReG=10,000. With the aid of tomographic particle image velocimetry, the suppression of the coherent structures due to this fractal geometry is analysed and the changes to the near-field vorticity are evaluated. This particular geometry leads to the breakup of the azimuthal vortex rings present for round jets and to the formation of radial and streamwise opposite-signed patches of vorticity. The latter are found to be responsible for the axis switching of the jet, a phenomenon observed for some noncircular jets where the major axis shrinks and the minor one expands in the near field, effectively switching the two axes of the jet. This was the first time, to the knowledge of the authors, that axis switching has been observed for a jet where the coherent structures have been suppressed. Following the significant differences found in the near field, the far field is examined. There, the integral lengthscale of the large scale eddies Lur and the size of the jet evaluated in terms of the jet half-width r1/2 are found to evolve in a similar fashion, whilst the ratio Lur/r1/2 is found to be higher for the fractal jet than for the round jet, for which the near-field structures have not been suppressed.