In this article, we propose a new method of three-dimensional data plotting based on the use of mixed hue palettes, which makes it possible to distinguish simultaneously both huge and subtle changes in the value of the presented quantity at the same plot. This method called "braid plot" is based on the alternating use of multiple palettes of colors (a kind of interlacing), which greatly increases the sharpness of the graph and allows us to define areas of equal values more accurately than using traditional graphs with a single palette or contour plot. We present here an algorithm of preparing braid plot composed of any number of initial color sets. As a result of using this type of plot, it was possible to detect, e.g., weak perturbation effects or subtle oscillations of the spectral density function, which is very hard to observe using classical plots.