Triangle Inequality Average - Mandelbrot Fractal Mini

Uploaded January 2020 | Updated September 2026, 2 weeks ago

A colouring method featured on Maths Town for the first time. The TIA is a very popular colouring method for making still images, but not so popular for videos because it is a little hard to control the colour as we zoom in. I have made some videos with variations on this method, but this time you find it in it's true form. A little shading is added to give the features more definition in the later parts of the video. Hopefully I can produce some more interesting results with this method. Please hit subscribe, and let me know what you think.

Thank-you to my supporters on Patreon.

/********************************************************************************
Patreon: patreon.com/mathstown (Support, Downloads & Usage Rights)
Website: https://www.maths.town
Twitter: twitter.com/MathsTown
********************************************************************************/

Music from Epidemic Sound: epidemicsound.com/referral/ekoiev

Triangle Inequality Average - Mandelbrot Fractal Mini - Zoom (8k 60fps)

$The Slow Burn - A Burning Ship Fractal Zoom Some creative colouring of the Burning Ship makes this one a little different. We also do a 100,000% stretch to find some hidden detail in the spires. Sorry, I havent uploaded in a while, I needed a little rest. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** OpenSea: https://opensea.io/collection/maths-town Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) Grab a T-Shirt: https://amzn.to/3eIfqmX Website: https://www.maths.town ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$

Colourless Forms - Mandelbrot Fractal Zoom Out

$Infinity Liquid II - Mandelbrot Fractal Zoom It has been a while since Ive uploaded, but perhaps it is worth the wait. I really like this one. This one will probably look best at 4k, so adjust your settings. There are a couple of minibrot passes to check out also. There is even a big render glitch, let me know if you see it. Thank-you to my supporters on Patreon. As usual, presented with mid-roll ads disabled. Let me know if you appreciate this! This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown If you liked this video you can buy me a coffee on Ko-Fi: https://ko-fi.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Direct Donation: https://donate.stripe.com/7sI9DOaJ96wadpu9AC Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ (Easily the best source of music for creators!) #Mandelbrot #fractal #mathstown #fractals$ $Mindscape - A Mandelbrot Fractal Zoom A journey for the mind! Take your mind to another place during these crazy times. Graphically, it is a slow start, skip to the middle if you are short on time. This is a collobaration with dumbledog, a musician, long-time supporter and patreon who has appeared on this channel a few times before. An epic and amazing track from him this time called The Quiet Sun. Please subscribe. One unexpected bonus about this channel is getting to sample of the works of small independant creative musicians. There are some incredibly talented people working in generas that I would never normally investigate. Please consider giving dumbledog your support, and other independant artists, by buying some of their tracks. https://dumbledog.bandcamp.com Other videos on my channel featuring dumbledogs work: https://www.youtube.com/watch?v=ThHRh6nDvc0 5000 Subscribers Part 1 (currently the deepest zoom on this channel) https://www.youtube.com/watch?v=K8IQD16Vo-Y 5000 Subscribers Part 2 (currently the deepest zoom on this channel) https://www.youtube.com/watch?v=BMt8wzztsng Disciples https://www.youtube.com/watch?v=wo82S2vqQzw Orbit of Complexity Follow dumbledog here: Bandcamp: https://dumbledog.bandcamp.com YouTube: https://www.youtube.com/user/ItsTheTaterCam This video was rendered and uploaded in 8k @60fps. Im not sure if YouTube is allowing long 8k video at the moment? Anyway, fractals look better rendered at higher resolutions becaue it reduceses artefacts, so this should look really nice at 4k. Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music by: dumbledog$ $Unusual Symmetry - Perpendicular Mandelbrot Fractal Zoom (4k 60fps) Sometimes things are just so perfect that they dont need improving. This fractal zoom has no clever lighting or colouring effects, it just uses the normal escape time colouring that you have seen 1000 times before. However this is not the Mandelbrot Set, rather its beautiful sister the Perpendicular Mandelbrot fractal, which has some beautiful shapes and unusual symmetry. The deep imagery is really nice, so I put it first, we are zooming out today! Enjoy! And please hit subscribe. Rendered in glorious 4k! As usual, this video is best viewed at high-resolution. Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ Look to the Stars - Johannes Bornlof When In Doubt - Johannes Bornlöf Dancing in the Rain - Johannes Bornlof Software: Kalles Fraktaler and my own KMovieMaker plug-in for After Effects. https://www.maths.town/after-effects-plugins/kfmoviemaker$ $Mandelbrot World Record Attempt - Part 8 (e14000 to e16000) 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$ $Audio - An Audio Responsive Mandelbrot Fractal zoom Another little experiment for you this Friday... I hope you dont mind me publishing the experimental stuff, but I know a few Patreons have been waiting for this. Ive lots of requests to make the fractals respond to audio, and Ive finally got it working. Now that is possible to control most parameters based on audio, there are several interesting possibilities for musicians trying to generate visuals. This video is not perfect, but the proof of concept is there. It is the last main feature I wanted to add to my little After Effects plug-in before I get is published on the website. Hopefully over the coming month, Ill get it online, and tutorials published so that you can do it yourself. (Patreons will be the first to know). I dont anticipate doing too many audio based zooms myself. Please hit subscribe! Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/Music:$

Left of Centre - A Julia Set Fractal Zoom

$Power of Four - 4th Power Mandelbrot Fractal Zoom The Quadbrot! Or the fourth power Mandelbrot set which features embedded Julia Sets with 4-way symmetry. Enjoy! Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Grab a T-Shirt: https://amzn.to/3eIfqmX ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals #quadbrot$ $Unstable Orbits of the Mandelbrot Set (Orbit Splines) In this video we explore a hidden aspect of the Mandelbrot Set. For every single pixel in my videos there is an orbit. That is the path the value of z takes as we iterate over z=z^2+c. Normally, you dont see this, it is just something I calculate. In this video we use these values as control points to build a spline (curved line). Each spline represents a single point outside the Mandelbrot Set. (The inside points are usually less interesting, but see the Spline Brot video to get the idea. https://www.youtube.com/watch?v=hNVlygTyWEo ) There are 10 different orbits featured in this video. Actually, they are quite small, only around 1000 iterations. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals Made with #blender .$