Julia Sets of the 2nd Power Mandelbulb Fractal - A Study @MathsTown

Julia Sets of the 2nd Power Mandelbulb Fractal - A Study @MathsTown

Uploaded June 2024 | Updated September 2026, 2 weeks ago

A little bit more a of a mathematical curiosity for you in this video. There isn't much information published about these Julia Sets, so I thought I would publish a demonstration here. Just a simple render, with simple material; sometimes simplicity is nice.

This video shows the Julia Sets of the Mandelbulb (2nd Power). Only the y and z coordinates are changing, so we see the set of symmetrical Julia Sets. Modifying the x coordinate introduces a twisting type motion, which is not shown. The coordinates are shown in cartesian and spherical form at the bottom. The parameter slowly spirals outwards through the video, meaning the sets become less dense as the video progresses.

Once I do a little more coding, I will release the code I used to create this as a plug-in for Adobe & OpenFX. Stay tuned if that is something that interests you, and you'd like to render your own.

Thank-you to my supporters on Patreon.

This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. patreon.com/mathstown

If you liked this video you can buy me a coffee on Ko-Fi: ko-fi.com/mathstown

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#Mandelbrot #fractal #mathstown #fractals

$Julia Sets of the 2nd Power Mandelbulb Fractal - A Study A little bit more a of a mathematical curiosity for you in this video. There isnt much information published about these Julia Sets, so I thought I would publish a demonstration here. Just a simple render, with simple material; sometimes simplicity is nice. This video shows the Julia Sets of the Mandelbulb (2nd Power). Only the y and z coordinates are changing, so we see the set of symmetrical Julia Sets. Modifying the x coordinate introduces a twisting type motion, which is not shown. The coordinates are shown in cartesian and spherical form at the bottom. The parameter slowly spirals outwards through the video, meaning the sets become less dense as the video progresses. Once I do a little more coding, I will release the code I used to create this as a plug-in for Adobe & OpenFX. Stay tuned if that is something that interests you, and youd like to render your own. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown If you liked this video you can buy me a coffee on Ko-Fi: https://ko-fi.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $Crystal Beats - A Mandelbrot Fractal Zoom (Guest Artist: LitLot) [Watch in 4k+!] (Watch in at least 4k to avoid compression artefacts) Today we have a special guest artist on the channel, my 7-year-old daughter, and fractal lover LitLot. She found the path through the Mandelbrot, chose the colour scheme, paired is with the Mosaic colouring algorithm, and chose the music. This video has a lot more energy that my usual style! If youd like her to keep designing videos, give a shout out in the comments. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ Model Face - Ooyy Lucid Dreaming - Ooyy #Mandelbrot #fractal #mathstown #fractals$ $Nostalgia - Mandelbrot Fractal Zoom A simle classic Mandelbrot zoom. I quite like the shapes and patterns that occur in this area of the Mandelbrot, so I thought Id keep it clean and simple. Enjoy! As usual, no mid-roll ads. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$

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$Edge - A Mandelbrot Fractal Zoom Throwng a little noise at the edges of the colour and cycling them makes for quite an interesting effect. Enjoy! Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $Classic 10 - 10th Power Mandelbrot Fractal Zoom Welcome to the start of our classic powers count down. Each fortnight (Monday) I will release a new video, exploring a different power of the Mandelbrot equation. We will count down from 10 to 2. Each video will have classic escape time colouring (plus maybe a smidge of slope shading). This is a deep one, to start things rolling, in fact Im pretty sure it is the deepest 10th power zoom ever made. Its a bit repetitive, sorry, and not all the videos will be so long. I call this fractal the decabrot, but that is by no means an official term. The normal equation is z=z^2+c, but this fractal uses the equation z=z^10+c. The embedded Julia Sets all have 10-way symmetry, and there are lots of 10 way features to be found in this one. The fractal itself, and the mini-decabrots, all have 9 bulbs, which is an interesting contrasts. Thank-you to my supporters on Patreon. For Patreons I am hoping to publish reversed zooms of each of these classic videos. So you can enjoy zooming out if you prefer. The higher powers are quite good in reverse, because there is less circular stuff around the minibrot. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/$

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$Golden Outlines - A (Stretched) Burning Ship Fractal Zoom A stunning Burning Ship fractal zoom featuring golden outlines! This fractal is not only beautiful to look at, but it also utilizes the distance estimation colouring algorithm, making it an impressive example of the power and beauty of mathematics. In this video, we take you on a journey through the intricate and ever-changing patterns of the Burning Ship fractal. The golden outlines of the fractal stretch and twist, creating an otherworldly and hypnotic effect. The zoom takes you deeper and deeper into the fractal, revealing new layers of complexity and detail with each passing moment. So sit back, relax, and let yourself get lost in the intricate and stunning world of the Burning Ship fractal. Happy New Year! Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #BurningShip #mathstown #fractals Tezos Art Collectors can support me by purchasing a related NFT on Teia (all 1 tez): https://teia.art/objkt/804551 https://teia.art/objkt/804550 https://teia.art/objkt/804436 https://teia.art/objkt/804434 https://teia.art/objkt/804433$ $Mandelbrot World Record Attempt - Part 5 (e8000 to e10000) The deepest Mandelbrot zoom ever! This zoom is over 24-hours long, uploaded to YouTube in 11 parts. It will finish on a mini-Mandelbrot. As such, I am claiming a world record for the deepest Mandelbrot video! I have kept to the traditional colouring style for this one. Consider playing your own music while you let this one roll. Sit back, relax, and soak it in. This will be the only time I ever attempt a video this deep. Rendering around the final mini-Mandelbrot is just too computationally expensive to try again; I have other things I wish to achieve now. If you wish to claim the deepest Mandelbrot title, and would like me to acknowledge it, here are my conditions: It must finish on a mini-Mandelbrot, it must be rendered in at least 4k, it should double in depth no faster than once per second, and you should publish the coordinates. Finally, a huge thank-you to my supporters on Patreon, and my loyal subscribers who have made this channel possible! If it wasn’t for you, this content would not exist. I always turn off mid-roll ads so you dont get interrupted! You can support this practice by joining Patreon, super-thanks, or making a direct one-time donation: https://donate.stripe.com/7sI9DOaJ96wadpu9AC Here are the links for each part (the release will be spaced) Part 1: https://youtu.be/CfqHAOOM8Tw Part 2: https://youtu.be/Ac33rIHr4xI Part 3: https://youtu.be/Os2SC5PHQ8Y Part 4: https://youtu.be/DVoShta1v6o Part 5: https://youtu.be/qzHrFROrQS4 Part 6: https://youtu.be/gg9hd4Kh-tQ Part 7: https://youtu.be/1I35JnVUNk8 Part 8: https://youtu.be/wFoV2rQSIMo Part 9: https://youtu.be/h4quecQTfds Part 10: https://youtu.be/Hm9011pZw9I Part 11: https://youtu.be/6Z-qXe9-3Fs Full playlist of this zoom: https://www.youtube.com/playlist?list=PLKHNByHfHxT4Gl01oxGmuK5UGPkbUTjll This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel or commercially if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Direct Donations: https://donate.stripe.com/7sI9DOaJ96wadpu9AC Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ (Easily the best source of music for creators!) #Mandelbrot #fractal #mathstown #fractals$

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Julia Sets of the 2nd Power Mandelbulb Fractal - A Study