Szegedi Butterfly fractals is a family consisting of two fractals, (admittedly unimaginatively) named Butterfly 1 and Butterfly 2, as well as from their Julia duals. Their name comes from the sole fact that they resemble butterflies to me. They are, however very compex fractals with many landscapes to discover. Their Julia duals are also magnificent. Below you will find images of these two fractals, as well as some zooms into their interesting areas, as well as the pictures of some of their Julia duals.In the future, I hope to manage to get enough time to submit more interesting landscapes of these sets.
You can read the story about the original discovery, the fading, and the renaissance of these fractals here.
For those interested in generating these beauties themselves, Fractint and Ultra Fractal formula files are also provided at the bottom of the page.
Overview Pictures 

Szegedi Butterfly 1 
Szegedi Butterfly 2 
Zoom Pictures of Szegedi Butterfly 1 

Zoom Pictures of Szegedi Butterfly 2 

more to come soon... 

Pictures of Szegedi Butterfly 1 Julia duals 

more to come soon... 

Pictures of Szegedi Butterfly 2 Julia duals 

more to come soon... 

Formulae 

Below are the formula definitions of the Szegedi Butterfly fractals, presented in the Ultra Fractal syntax. They'll work if typed directly into Ultra Fractal. You are encouraged, however to download the official formula files from the section below since they also contain other preset parameters.  
Szegedi Butterfly 1 
Szegedi Butterfly 2 
SzegediButterfly1 {
(sqr(x)  sqrt(abs(y))) * 1i + #pixel

SzegediButterfly2 {
(sqr(y)  sqrt(abs(x))) * 1i + #pixel

Download formula files 

Download the Ultra Fractal formula file for
Szegedi Butterfly fractals, or Download the Fractint formula file for Szegedi Butterfly fractals. 
Tips for explorers 
