The Power of Phi - Fractional Power Mandelbrot Zoom @MathsTown

Uploaded March 2020 | Updated September 2026, 2 weeks ago

Another very little instalment in the fractional power Mandelbrot series. This time phi (1.6180339887), as it has been requested a lot. Phi is quite a famous constant, but in this context it has no special meaning. This is what the fractal z= z^(1.6180339887) + c looks like. Like all non-integer powers, the fractal is smashed into pieces, because there are branch cuts in the original function. Please hit subscribe.

(These are costly to render, so I keep them short).

Thank-you to my supporters on Patreon.

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Music from audionautix.com (creative commons)

You may use this particular video under the Creative Commons Attribution license. (this only applies to some videos on the channel).

$The Power of Phi - Fractional Power Mandelbrot Zoom Another very little instalment in the fractional power Mandelbrot series. This time phi (1.6180339887), as it has been requested a lot. Phi is quite a famous constant, but in this context it has no special meaning. This is what the fractal z= z^(1.6180339887) + c looks like. Like all non-integer powers, the fractal is smashed into pieces, because there are branch cuts in the original function. Please hit subscribe. (These are costly to render, so I keep them short). Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from https://audionautix.com (creative commons) You may use this particular video under the Creative Commons Attribution license. (this only applies to some videos on the channel).$

Skeletons - Halloween Special Mandelbrot Fractal Zoom (8k 60fps)

$The Hardest Trip II - 100,000 Subscriber Special To celebrate reaching 100,000 subscribers Ive tried to make a sequel to the most popular video on Maths Town: The Hardest Trip. Same colouring, same music artist, a bit deeper, and a few less iterations. Thanks to everyone who has supported the channel over the last few year. 100,000 subscribers is a huge milestone for such a niche channel! Your support is most appreciated! As usual, presented with mid-roll ads disabled so you can simply enjoy. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) Website: https://www.maths.town ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $Art Therapy - A Mandelbrot Fractal Zoom Slowing it down today for those who like some calming fractal meditation. Sit back, relax, and enjoy. This is quite an interesting location as we drop through the crack of a mini-Mandelbulb, this creates some interesting spiral effects in the late video. Presented without mid-roll ads for uninterrupted enjoyment. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ (Easily the best source of music for creators!) #Mandelbrot #fractal #meditation #mathstown #fractals$ $Julia Sets of the 2nd Power Mandelbulb Fractal - A Study A little bit more a of a mathematical curiosity for you in this video. There isnt much information published about these Julia Sets, so I thought I would publish a demonstration here. Just a simple render, with simple material; sometimes simplicity is nice. This video shows the Julia Sets of the Mandelbulb (2nd Power). Only the y and z coordinates are changing, so we see the set of symmetrical Julia Sets. Modifying the x coordinate introduces a twisting type motion, which is not shown. The coordinates are shown in cartesian and spherical form at the bottom. The parameter slowly spirals outwards through the video, meaning the sets become less dense as the video progresses. Once I do a little more coding, I will release the code I used to create this as a plug-in for Adobe & OpenFX. Stay tuned if that is something that interests you, and youd like to render your own. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown If you liked this video you can buy me a coffee on Ko-Fi: https://ko-fi.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $Crystal Beats - A Mandelbrot Fractal Zoom (Guest Artist: LitLot) [Watch in 4k+!] (Watch in at least 4k to avoid compression artefacts) Today we have a special guest artist on the channel, my 7-year-old daughter, and fractal lover LitLot. She found the path through the Mandelbrot, chose the colour scheme, paired is with the Mosaic colouring algorithm, and chose the music. This video has a lot more energy that my usual style! If youd like her to keep designing videos, give a shout out in the comments. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ Model Face - Ooyy Lucid Dreaming - Ooyy #Mandelbrot #fractal #mathstown #fractals$ $Nostalgia - Mandelbrot Fractal Zoom A simle classic Mandelbrot zoom. I quite like the shapes and patterns that occur in this area of the Mandelbrot, so I thought Id keep it clean and simple. Enjoy! As usual, no mid-roll ads. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$

A Simple Journey - Mandelbrot Fractal Zoom (7e1631)

Out of the Blue - Mandelbrot Fractal Zoom Out (1e1234)

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

Christmas Tree - A Mandelbrot Fractal Zoom