Almost all procedural textures in Blender use derivatives for calculating normals for texture mapping (with as exception Blend and Magic). The texture normal, the derivative, is calculated by using four samples in the texture formula:
s0= texture(x, y, z) s1= texture(x+nabla, y, z) s2= texture(x, y+nabla, z) s3= texture(x, y, z+nabla) normal= s0-s1 normal= s0-s2 normal= s0-s3
Up to now, the "nabla" offset was a constant (0.025) which worked fine in most cases, but doesn't give proper control over the way a texture is sampled, for example to make the effect smoother or sharper. This feature especially is useful in combination with the ColorBand feature.