Cameron Browne. Impossible fractals

Although spirals are not fractals, they are briefly mentioned here as plane-filling curves that display aspects of self-similarity and variable resolution. Figure 16 (top left) shows a spiral version of the tribar; this is no longer an impossible figure but has a valid physical interpretation as a conical spiral.

Figure 16. A spiral tri-bar and hexagonally bound isometric spirals.

However, impossible spirals may be achieved by again using the isometric grid. The remainder of Figure 16 shows an isometric cube iteratively layered to produce impossible spirals of arbitrary resolution. These are similar to multibar designs, except that concentric layers share bars with their inner and outer neighbours (four colours are required). Each iteration maintains a perfectly hexagonal outline, making these isometric spirals suitable for tilings and other artistic applications.