First, I rotated the photograph so the butterfly is right-side up. I wanted an escaping butterfly, not one dribbling out the bottom!

Also we can get a fresh perspective when flipping an image.  If I'm too involved, I'll check it in a mirror or something to see how it balances.  Like walking around a chessboard: it helps yield a sense of dynamics, strengths, weaknesses.

Adjusting curves is normally better than adjusting contrast, but in this case, I wanted bold contrasts to clear out noise.

OK, the butterfly is there, but the eyes go to the brightest spot.  Since chaos is non-linear, I have to be especially aware of the line tracked by the eyes.  I want viewer's eyes to loop out and come back to the butterfly, repeatedly.  Fixing the focal point will come later, but it will require a few steps.