is a simple closed curve consisting of exactly three parabolic cusp points as well as three parabolic arcs, each connecting two parabolic cusps. Every parabolic arc of period k has, at both ends, an interval of positive length across which bifurcation from a hyperbolic component of odd period k to a hyperbolic component of period 2k occurs. Implementation The below pseudocode implementation hardcodes the complex operations for Z. Consider implementing complex number operations to allow for more dynamic and reusable code.For each pixel (x, y) on the screen, do: { x = scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.5, 1)) y = scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1, 1)) zx = x; // zx represents the real part of z zy = y; // zy represents the imaginary part of z iteration = 0 max_iteration = 1000 while (zx*zx + zy*zy < 4 AND iteration < max_iteration) { xtemp = zx*zx - zy*zy + x zy = -2*zx*zy + y zx = xtemp iteration = iteration + 1 } if (iteration == max_iteration) //Belongs to the set return insideColor; return iteration * color; } Further topological properties The tricorn is not path connected. Hubbard and Schleicher showed that there are hyperbolic components of odd period of the tricorn that cannot be connected to the hyperbolic component of period one by paths. A stronger statement to the effect that no two (non-real) odd period hyperbolic components of the tricorn can be connected by a path was proved by Inou and Mukherjee. It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. On the other hand, the rational parameter rays at odd-periodic (except period one) angles of the tricorn accumulate on arcs of positive length consisting of parabolic parameters. Moreover, unlike the Mandelbrot set, the dynamically natural straightening map from a baby tricorn to the original tricorn is discontinuous at infinitely many parameters. References Fractals