i use mandelbulb3d to render my fractals. The software is free, and you can download it Here.

In the tutorials section I explain some aspects of the software, however, there are far better tutorials around that cover the basics of the ui.

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Bio

Julius Horsthuis (Amsterdam, 1980) is a Visual Effects designer and Fractal artist.

Julius developed a love for film and video at the age of 12. After high school, he worked on various film sets as sound recordist, clapper loader and focus puller in the years 2000 to 2006. Baantjer (2000-2003), Flirt (van Eyck, 2005) Koppels (2006). He also finished a one year video study in the Open Studio (2003)
Meanwhile, Julius had developed interest in computer graphics. He worked for several years for different (post) production companies, Revolver (2004-2005) Carbon (2006-2010) and Hectic Electric (2010-present).
Years of experience on the movie set proved invaluable, for Hectic Electric worked intensively on the VFX of many big films, such as “De Storm” (Sombogaart, 2009). At Hectic, Julius worked on several films, such as “Sonny Boy”  (Peters, 2011) and “Nova Zembla” (Oerlemans, 2011) He took creative supervision on what was the most VFX-heavy film in the Netherlands: “Koning van Katoren” (Sombogaart, 2012)
Upon its release, the critics specifically praised the Visual Effects in the film; something that is unfortunately not often the case in the Netherlands. The movie also won the VNAP VFX award for best VFX in a Dutch film.
In 2014, Julius started experimenting with Fractal Environments. As a Fractal Artist, he has created Fractal short films, and Immersive Experiences, which have been exhibited in galleries and film festivals around the world, such as the IX symposium in the Satosphere in Montréal, the Cineglobe film festival in CERN and the Geneva Tous Ecrans festival.
Online, Julius' fractal art has been picked up or covered by international blogs such as The Creators Project, Motionographer, Gizmodo, and the Vimeo Staff picks. His experimental Virtual Reality experiences featured on the Oculus Rift website upon release, and became some of the best rated VR-experiences on the site.