The Stripe color scheme produces images similar to those produced by curvature but were different enough for us to include in the program. This color scheme tracks the orbit of the point and creates a normalized value of the sine of a constant times the argument of the orbit point. Specifically, we calculate 0.5 sin(k arg(zn)) + 0.5 for each of the points in the orbit. The program takes the average of these values over the orbit of the point. The value of k is the stripe density, this can be any real number but usually positive integers are used. Due to the pre-calculation design of this program and the amount of storage needed for this method we have restricted the values of the stripe density to be 1, 2, and 3. Although this may seem very restrictive, these stripe densities, with the elongation affect produced by changing the bailout radius, produce a wealth of different images. In addition, when the stripe density is set larger the stripes produced become "busy". As with curvature, this method does not tend to be very interesting for the inside points so we have included it only in the plotting of outside points.
The program offers two interpolation modes linear interpolation and Catmull-Rom Spline interpolation. These interpolation methods make the transition over iteration levels continuous and produces unbroken streams of color. Linear interpolation combines the last and next to last values and the Catmull-Rom Spline interpolation uses a cubic spline through the last four orbit values. These interpolation methods assume that the dynamical system is based on a polynomial iterative function, i.e. az^n + bz^k + ... + c where the exponents are real number constants. Thus, when using non-polynomial systems the results are not as spectacular. The Interpolation Degree should be the same as the degree (highest power) of the polynomial-like function. So for the Mandelbrot set the degree should be 2 and for z = z^1.5 + c it should be 1.5.
Note: This coloring scheme does not tend to work very well in a convergence bailout mode. Also, to achieve the smoothness, a fractional escape iteration needs to be estimated. The same estimate is done here as for the polynomial smoothing algorithm in the iteration color scheme, hence the curvature coloring works best for polynomial-like systems. One can apply the method to non-polynomial systems with varying success but you almost always see discontinuous coloring. One final note, you will want to use a large bailout radius with this method, a radius of 1000 or even 10^10 is not uncommon. With a small radius you will see the propagation of errors close to the iteration level changes. Also, the larger the bailout radius is the longer the color streaks tend to be.