coloring by closest approach distance

[Khashishi]

I made a coloring formula for escape time fractals which is very simple but I think it looks pretty. It works for both inside and outside points. I wouldn't be surprised if someone did this before.

Basically, for each pixel, we calculate the orbit and keep track of the minimum distance between the orbit and the origin, and the minimum distance between the orbit and the axes (the lines x=0 and y=0). Then we choose a color based on some linear combination of the two distances. If you only use the distance to the origin, you get these circular halos around each minibrot bulb. If you only use the distance to the axes, you get these stalks coming from the bulbs. With the sum of both, you get these horns coming out of each part, and it looks pretty.

I'm new to this forum, so I don't know if this image will work. I think I originally calculated this image in Fractint, but I lost the Fractint files. It's a mandelbrot fractal. The outside coloring was as above. The inside coloring was bof61.

https://www.dropbox.com/s/5vffg35gzlqai0t/Orixes%20Mandelbrot.png?dl=0

It's best to set the bailout to a high number; otherwise, the horns get truncated.
I implemented it in ChaosPro as a color formula file. The formula is called Orixes.

Code:

Orixes
{
parameter real axis_scale;
parameter real origin_scale;
real axis_d;
real origin_d;

	void init(void)
	{
		axis_d=9e99;
		origin_d=9e99;
	}
	void loop(void)
	{
		if (cabs(z)<origin_d)
		{
			origin_d=cabs(z);
		}
		if (abs(real(z))<axis_d)
		{
			axis_d=abs(real(z));
		}
		if (abs(imag(z))<axis_d)
		{
			axis_d=abs(imag(z));
		}
	}
	void final(void)
	{
		index=axis_d*axis_scale+origin_d*origin_scale;
	}
	void description(void)
	{
		this.title = "Origin and Axis distances";
		
		axis_scale.caption="Axis distance scaling";
		axis_scale.default = 0.7;
		axis_scale.hint = "Color scaling for distance between orbit and either axis";
		
		origin_scale.caption="Origin distance scaling";
		origin_scale.default = 0.3;
		origin_scale.hint = "Color scaling for distance between orbit and origin";
	}
}

[quaz0r]

 

https://en.wikipedia.org/wiki/Pickover_stalk

[Khashishi]

I see. I knew I didn't come up with it first

[quaz0r]

regardless, still always fun to discover something on your own