Visualization of four-variable algebraic equations representing form and coloration simultaneously

In the beginning of the four variables algebraic equations research two problems were faced. Having more variables then equations in the equations set for visualization is the first one. Having several roots of the color equation which should be shown by one color value is the second one. In the given article results of solving these problems are represented. Different methods of setting relation between colour equation roots and colour in the point are esteemed. Examples of colouring the algebraic surfaces by adding a forth variable to its equation, examples of painted surfaces as well.