This is Behind the Scenes for Basics of Flame Fractals.
This was made by using six shape transforms, each with a post transform to move it to one of the spots in the final picture. A test gradient is used here that is similar to the one used in the article, but it has eight colors instead of four. Feel free to use it for your own testing.
I started with the basic framework explained in the article, using horseshoe for the first transform. I increased the variation value and tweaked both transforms to get this design, then rotated the camera 90°. The gradient is from a collection by WendyTsukino.
Parameters for the other images are either in the referenced flame pack, or derived from it as described in the article.
The spiral style described in this article is simple, and probably independently discovered by anyone who does a bit of playing in a flame fractal program. So although this article is based on my own study, I don’t take credit for the style; it has been done before by many fractal artists.
An alternate method for getting the sweet spot in the center of a spiral is to move the initial shape up (actually, any direction will work) using a post transform. Then the linear that creates the spiral needs only to rotate and shrink the fractal, not move it; this will put the center of the spiral at the origin. This has the advantage that rotating the transform doesn’t move the center. Here is a starting point with the first transform moved up and to the left:
Parameters at https://pastebin.com/BcbqJzvP.