I'm happy to present you the gallery of the complex-valued Weierstrass function! As you may remember, the Weierstrass function is defined as a sum of cosines with exponentially increasing frequencies and exponentially decaying amplitudes. Now let's replace the cosines cos(t) with complex exponentials cos(t) + i sin(t). For a non-integer frequency ratio, the function is aperiodic and does not form a closed curve on the complex plane. But for some parameter values, curious patterns start to emerge as we plot the function. This is the process behind the images. They may not look like it, but each of them is just a very long curve! Because the curves have to be very long to achieve high quality, the rendering is computationally demanding.
I found that the most aesthetically pleasant shapes lie at the boundary of fractality (equal frequency and amplitude parameters, fractal dimension = 1). I'm still trying out various frequency parameters, so there is more to come.