Ridges and waves for Model 1hf. We show the time evolution between 0 and 3 Gyr (indicated in the first column) of the disc region at ϕ = π ± 0.2 rad (marked with dotted lines in Fig. 3). First column: a normalised density histogram of the radius of the particles R. Second and third columns: the R − V_ϕ projection in density and coloured by mean V_R, respectively. Fourth column: the particles in the L_Z − V_R projection. The vertical dashed lines in all panels indicate the prediction of the spiral arm locations following a winding rate of .