Different approach on rendering julia-/mandelbrot set

[TheRedshiftRider]

Hello,

I've been thinking about a different way of rendering juliasets:

-Pick ONE coordinate on the complex plane and calculate the new one with the standard function (with the variable c in it.).
-Then connect these two coordinates and use all (visible) points on that line to repeat these two steps.
-For the colouring there are no differences. Same for the bailout norm.


I'm not sure about what pattern this will be. Would this be give a different result than the standard sets?

[claude]

Not 100% sure on what you are plotting, per pixel escape time?  or forward iteration (which will give the attractors in the Fatou components)? or backward iteration? (which will give the Julia set wherever you start afaik)

assuming you're plotting pixels by escape time, and choosing which pixels to plot by drawing lines using forward iteration (and drawing lines by forward iteration from each of those points, recursively):
from least likely to most likely:

1.  the point you pick happens to be a fixed point - then the second point is the same as the first, and your image is just a point.
2.  the point you pick happens to be a chaotic point in the Julia set - then all subsequent iterates of that point are in the Julia set and it never repeats, so your image will contain the whole Julia set and possibly most of its interior and exterior too
3a. the point is far outside the filled-in Julia set, then subsequent points will escape, but depending on the transformation of your start point you might get a line that passes through the Julia set, so you'd probably end up covering the plane with lines and getting a regular image
3b. the point is far inside the filled-in Julia set, then it depends heavily on the period of its attractor - if it's 1, then it's a fixed point and nothing interesting will happen, if it's more than 2 then the line will cross the Julia set and give you some exterior pixels to iterate and cover the plane with lines as in 3a, if it's 2 I'm not sure