Szegedi Butterfly fractals

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


(click for larger image)


(click for larger image)

 


Zoom Pictures of Szegedi Butterfly 1


(click for larger image)


(click for larger image)


(click for larger image)


(click for larger image)


(click for larger image)


(click for larger image)


(click for larger image)


(click for larger image)


Zoom Pictures of Szegedi Butterfly 2


(click for larger image)

more to come soon...


Pictures of Szegedi Butterfly 1 Julia duals


(click for larger image)

more to come soon...


Pictures of Szegedi Butterfly 2 Julia duals


(click for larger image)


(click for larger image)

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 {
init:
  z = #pixel
loop:
  float x = real(z)
  float y = imag(z)
  z = sqr(y) - sqrt(abs(x)) + 
           (sqr(x) - sqrt(abs(y))) * 1i + #pixel
bailout:
  |z| <= @Bailout
default:
  param Bailout
    caption = "Bailout Value"
    default = 127.0
  endparam
}
SzegediButterfly2 {
init:
  z = #pixel
loop:
  float x = real(z)
  float y = imag(z)
  z = sqr(x) - sqrt(abs(y)) + 
          (sqr(y) - sqrt(abs(x))) * 1i + #pixel
bailout:
  |z| <= @Bailout
default:
  param Bailout
    caption = "Bailout Value"
    default = 127.0
  endparam
}

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

  • To get high contrast colors In Ultra Fractal, try alternate colorings, or select a higher color density (8 usually works fine).
  • These fractals are actually asymmetric, altough they appear symmetric on the first sight! Zooming in reveals that the seemingly symmetric parts are actually quite different.
  • The border area of the convergent lake is very noisy. Increasing the maximum iteration limit will reveal new dots of divergency, and increasing the maxiter even more will reveal that these dots form a weblike structure.
  • Don't use guessing algorithms for rendering the border area, because it will miss out many details.

All content on this site (c) 2002 Attila Szegedi (szegedia at freemail dot hu). All rights reserved.