Space-filling fractal square grids fitted at the entrance of a wind tunnel’s test section generate unusually high Reynolds number homogeneous isotropic turbulence which decays locked into a single length-scale l. Specifically, during turbulence decay along the streamwise coordinate x, E11(k1,x)=u′2lf(k1l) over the entire range of wavenumbers, where l and the function f are about the same for all the grids tried here. As a result, this fractal-generated turbulence has the following properties which we have also observed in the decaying region: L∕λ is constant, independent of the x grid and Reλ; ϵ∼Reλ−1u′3∕Lu; and E11(k1)∼(u′3∕Lu)2∕3k1−5∕3 instead of E11(k1)∼ϵ2∕3k1−5∕3 in the observed range of wavenumbers where f(k1l)∼(k1l)−5∕3.