Unstable Orbits of the Mandelbrot Set (Orbit Splines) @MathsTown

Uploaded March 2023 | Updated September 2026, 2 weeks ago

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 don't 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. 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. patreon.com/mathstown

/********************************************************************************
Patreon: patreon.com/mathstown (Support, Downloads & Usage Rights)
Website: https://www.maths.town
Twitter: twitter.com/MathsTown
Discord: discord.gg/YphYVt787v (Drop by and say hello)
********************************************************************************/

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

#Mandelbrot #fractal #mathstown #fractals

Made with #blender .

$Unstable Orbits of the Mandelbrot Set (Orbit Splines) In this video we explore a hidden aspect of the Mandelbrot Set. For every single pixel in my videos there is an orbit. That is the path the value of z takes as we iterate over z=z^2+c. Normally, you dont see this, it is just something I calculate. In this video we use these values as control points to build a spline (curved line). Each spline represents a single point outside the Mandelbrot Set. (The inside points are usually less interesting, but see the Spline Brot video to get the idea. https://www.youtube.com/watch?v=hNVlygTyWEo ) There are 10 different orbits featured in this video. Actually, they are quite small, only around 1000 iterations. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals Made with #blender .$ $By the Ocean - Burning Ship Fractal Zoom A quiet journey into the Burning Ship fractal. The fractal is significantly stretched, so I started the video from the point of stretching. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #BurningShip #fractal #mathstown #fractals$ $The Power of Tau - Irrational Power Mandelbrot Zoom (n=6.28) A little mathematical curiosity for you today, a fractal made with a non-integer component. (z=z^τ + c). Tau (τ) is a mathematical constant equal to 2π. Tau is the ratio of a circle’s circumference and its radius, approximately 6.28. Actually, tau is not in popular in mathematics, the use of π is far more common. (π is the ratio of the diameter to the circumference). Here we use tau as the exponent (instead of 2) in the common Mandelbrot formula. Such use has no significant meaning other than general curiosity, but it does give us good excuse to inspect a fractal with a fractional exponent. These fractals are full of branch cuts. Please hit subscribe! Im slowly building a website, Im going to try and publish more detailed information about each video. About this video: https://www.maths.town/videos/the-power-of-tau-video Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music: SoloAcoustic5 by https://audionautix.com (Creative Commons)$ $Alpha - A Mandelbrot Fractal Zoom A new take on the Mandelbrot zoom. Ive updated my software to include alpha channel generation so I can use a little transparency. This was actually a little harder to get smooth than I expected. Skip forward a ca little if you are short on time as this ones takes a moment to become more interesting. Enjoy! Some ambient music added to this one for a more relaxing experience. 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 Location: Re: -1.9415724275898197731159808618178240603041671456558596029234314466269124547350802346918377819508160686518145022812659003195271206857136805357446723836410837519229650306155482459715074821128222535874637257409874203344155597016717755271385511524458619316790193728174514672360390330848881751400478615758671459756570124525945899065193327878327061360687523678982186262576885255687445945453234566843963334257447554427863259940652614709323842011838038231799355802858599961015007536523513542784389604788502317459030850586752100601287376157502688746791746846293285834368071617424717670260373933300872460608261288734283002940651883819867020085664952845825346 Im: -0.0002113593089272728075527340348912414862382021595483582128644841915909364948882066683039519098243117287960338376910293727379846807428176542919618431162471045349880209105271166833454515692868401257980639937916482160540325616967732150235729227308158911194243891619134654149470343142495165021120540344380975806682738276662879753646124900809427566348787804705412077065169560549572923743643166341976681545855066188193453823403142491301091871942245567355919057134225437810510013524769631761199513330105060068804503075771728559962214752419970766661391940448883091957306644579386511701974855380704418120751916708079210066399386823530951909699918887767143 Zoom: 2.1e621$

Arteries - Mandelbrot Zoom with Triangle Inequality Average (8k 60fps).

Christmas Tree 2020 - Mandelbrot Fractal Zoom

Line Trap - Mandelbrot Fractal Zoom [NFT]

$Classic 5 - 5th Mandelbrot Fractal Zoom A simple dense colouring for this 5th Power Mandelbrot fractal zoom. Ive just joined Amazon Merch, so you can grab a Mandelbrot T-Shirt there. https://amzn.to/3eIfqmX Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Grab a T-Shirt: https://amzn.to/3eIfqmX ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/$ $Pop - A Mandelbrot Fractal Zoom A fun little zoom with an orbit trap based colouring method. I felt like making something short and poppy after the last epic. I know a few of you has been asking for animated zooms again, I promise I will get back to that soon also. If you want to play with this method youll find it in Ultra Fractal and its called Gnarly Orbit Trap, Dist. Method (akl.ucl). This colouring method is found in Ultra Fractal and I believe that it was written by Andreas Lober and Mark Townsend. (Please note, I use custom code to assemble Ultra Fractal zooms, you wont get such a smooth output rendering every frame in UF. Ill try to put together a tutorial sometime, let me know if that is interesting for you.). Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown If you liked this video you can buy me a coffee on Ko-Fi: https://ko-fi.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Direct Donation: https://donate.stripe.com/7sI9DOaJ96wadpu9AC Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ (Easily the best source of music for creators!) This song: Two One Two - Ava Low #Mandelbrot #fractal #mathstown #fractals$ $Dreams - Mandelbrot Fractal Zoom A meditative journey into the Mandelbrot Set. A know a few of you enjoy fractals for relaxation and mediation, so Im trying something a little different today! A video that relies more on colour cycling than the actual colour. I was going for a dreamy feeling in this one. What are your thoughts? Please hit subscribe! As always, Ive requested that no mid-roll ads show during the video. I dont like interruptions! More info on this video (location etc): https://www.maths.town/videos/dreams-video Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ Bivack - Strom Avsked - Strom Ankomst - Strom Vandring - Strom Software: Kalles Fraktaler KFMovieMaker After Effects plug-in: https://www.maths.town/after-effects-plugins/kfmoviemaker$

Neon Lights II - Mandelbrot Fractal Zoom

$The Mandelbulb - 3D Fractal Tour in 8k This is the Mandelbulb Set. A true 3D fractal. This is my first publication of a 3D fractal. There is lots of cool 3D fractal artwork out there, but I just found there isnt many clean high-resolution renders of the basic fractals. So I went ahead and rendered it in 8k, so I could explore a little for myself. 8k is a somewhat ridiculous resolution at the current time, I probably wont do it again. I hope you enjoy it. There is no such thing as a 3D Mandelbrot Set. (There is a 4D quaternion one, but it is only as interesting as the 2D version) Thats because there is no 3D equivalent of complex numbers. However many attempts have been made to create one, the Mandelbulb is probably the most well known. This is actually the 8th power Mandelbulb which is considered the standard one. It displays stretching and squishing in places, much like some of the non-analytic 2D fractals (Burning Ship, Celtic, Etc). Please note: If you search YouTube for Mandelbulb you will mostly get fractal artwork that is not the Mandelbulb fractal, rather videos made with software of the same name. (Not used to create this video). Some nice vids out there. Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Grab a T-Shirt: https://amzn.to/3eIfqmX ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbulb #3d #8k #fractal #mathstown #fractals$