It all started off from a "flower" fractal randomly created by JWildFire. I tweaked it a bit and added some colors because it was rather monochrome to begin with and here is the point where it seemed ok to keep.

A good starting point

I wanted it to be more bright and impressive, so I changed the Layer Weight in the Coloring parameters (as @woodywood suggested in the past). Then I added some extra variations to make it more complex.

Not quite there, yet

I liked the bright colors but it seemed like the picture was all over the place, there was no real focus point. Yeah, a circle is surely making you focus there, and a sphere even more! A spherical variation gathered the vibrant colors in the middle and left the rest of the area darker, making the contrast I looked for.

Starting to be an eye-catcher

What good is a fractal if there are no tentacles?! I added some black tendrils and... oh yeah! That's an image I like, although it is a bit dark again...

After some more tweaks with colors & brightness, the way the tendrils are shaped, and the camera placement here is the final picture. To get really lost, get the detailed view (right-click -> open in new tab) and follow each tendril as it snakes around the picture...

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Flower Tentacles

by @nyarlathotep

A fractal made in JWildFire
(right-click -> "open in new tab" for detailed view)