Cartesian coordinates named after the mathematician René Descartes, are a system used to define the position of points in a plane or in space. In Cartesian coordinates, each point is represented by an ordered pair (x, y) in two-dimensional space or an ordered triplet (x, y, z) in three-dimensional space. The x-coordinate represents the horizontal position of the point, while the y-coordinate represents the vertical position in two dimensions. In three dimensions, the z-coordinate represents the position along the third axis, usually perpendicular to the plane defined by the x and y axes.

• In two-dimensional Cartesian coordinates:

  • The x-axis is the horizontal axis.
  • The y-axis is the vertical axis.
  • Points are represented as (x, y) pairs.
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• In three-dimensional Cartesian coordinates:

  • The x-axis, y-axis, and z-axis form a three-dimensional coordinate system.
  • Points are represented as (x, y, z) triplets.

Because the objects are created with maths formulas and they are not sculptures, the face orientation in Blender could be "wrong", means the face orientation is not in the way you would like to have them. XYZ Axis can be shown in the negative way and cause this problem. In the Blend File you find a Geometry node to solve this Problem. It´s called "Flipper", just put it on the end of the Modifier Stack.

Like in my other setups the Material Slot has NO use until you apply the modifier. The Materials are configured with the "set material Node" in the Geometry Node Setup and not with the material slot. If you work with new materials, you have to change in the "Material" Box in the Geometry Node Material Switch! (or after applying the Modifier). In this Blend File you´ll find 5 Materials for a "pre-setup", there is a special switch to change between them.