My entry to Apophysis Challenge #159, to use the hyperbolic variation with one other. I tried quite a few colors for the background; the flame colors are bright enough to work with a colored background. But I finally decided black worked best.

Tools and Resources
Apophysis 2.09 - flame generation and rendering
  Transforms: hyperbolic, pre_blur (built-in)
  Gradient: Fire_&_Ice-03-76 from BD's Fire & Ice
Postprocessing - Adobe Photoshop Elements 9
  Black background
  Reduce size using Bicubic Smoother to reduce some remaining jaggies

Parameters
<flame name="Rick-121130-2d" version="Apophysis 2.09" size="1000 800" center="0.024467213423232 -1.09512643565727" scale="1000" rotate="-3.5" oversample="1" filter="0.5" quality="50" background="0 0 0" brightness="5" gamma="4" gamma_threshold="0.05" >
<xform weight="0.5" color="0" hyperbolic="1.3" pre_blur="0.277" coefs="1 0 0 1 0 1.1" post="1 0 0 1 0 -0.8" chaos="0 " />
<xform weight="0.5" color="1" symmetry="0.738" hyperbolic="1" coefs="0.423331 -0.963553 0.963553 0.423331 0.994876 -0.6805" chaos="1 15 " />
<finalxform color="0" symmetry="1" hyperbolic="1" coefs="1.035796 0 0 1.035796 0.081855 0.097913" />
<palette count="256" format="RGB">
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</palette>
</flame>