Visual comparison of realistic physical fields and those sampled from maximum entropy models based on wavelet higher order moments $M¯$ and wavelet scattering spectra $S¯$ statistics. The first row shows five example fields from physical simulations of cosmic lensing, cosmic web, 2D turbulence, magnetic turbulence, and squeezed turbulence. The second and third rows show syntheses based on the selected high-order wavelet statistics estimated from 100 realizations. They are obtained from a microcanonical sampling with 800 steps. The fourth and fifth rows show similar syntheses based on the scattering spectra statistics, with only 200 steps of the sampling run. This figure shows visually that the scattering spectra can model well the statistical properties of morphology in many physical fields, while the high-order statistics either fail to do so or converge at a much slower rate. To clearly show the morphology of structures at small scales, we show a zoom-in of $128×128$ pixels regions. Finally, to quantitatively validate the goodness of the scattering model, we show the marginal PDF (histogram) comparison in the last row.