Celtic Mandelbrot Lab explores a variant of the classic Mandelbrot set — the 'perpendicular Mandelbrot' or Celtic variant. By taking the absolute value of the real component before squaring in the iteration formula (z → (|Re(z)| + i·Im(z))² + c), the fractal develops bilateral symmetry and intricate patterns reminiscent of Celtic knotwork and cross designs.
The modification breaks the standard Mandelbrot's rotational symmetry and introduces mirror symmetry along the real axis. This creates elaborate interlocking patterns at the boundary that echo the interlace motifs of Celtic art — hence the name. The shader uses smooth iteration count coloring with continuous potential to eliminate banding, producing gradient-rich visualizations of the escape-time fractal.
Interactive controls allow deep zoom navigation, iteration count adjustment, color palette selection, and animation of the Julia set parameter. The fractal reveals new symmetric structures at every zoom level.