The Logistic Map - Fractal Zoom @MathsTown

Uploaded October 2020 | Updated September 2026, 2 weeks ago

This video is a little demonstration that the Logistic Map equation is in the same family as The Mandelbrot Set. The Logistic Equation & Map come up a lot of places, such as biology where it can model the growth of animal populations. It also has many other uses. The Logistic Map, is the discrete version of the Logistic Equation (it is the recurrence relation.) If you are interested in this equation, how it appears in real life, and how it relates to the Mandelbrot, please see this great video by Veritasium:

"This equation will change how you see the world" youtube.com/watch?v=ovJcsL7vyrk

Equation: z = c*z*(1-z). [The initial value of z is 0.5].

Thank-you to my supporters on Patreon.

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

$Chilled Sunset - Perpendicular Mandelbrot Fractal Zoom Some chilled accoustic vibes for this sunset Perpendicular Mandelbrot Fractal Zoom. If you prefer to lift the tempo, feel free to play your own music. Ive scuffed the edges of this one by adding a little noise. What you your thoughts? Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown If you liked this video you can buy me a coffee on Ko-Fi: https://ko-fi.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $Spline-brot - The Internal Orbits of the Mandelbrot Set The Spline-brot is a new little concept Ive developed using data from the orbits of The Mandelbrot Set. This needs to be watched in 4k otherwise the YT compression kills it. Each wire is a spline built using the orbits of points in the Mandelbrot Set. The points of the orbit act as control points to build a NURBS spline. Anyways, something new and a little random. A fun little experiment. I hope you enjoy it. This video will not be uploaded to Patreon. /******************************************************************************** OpenSea: https://opensea.io/collection/maths-town Twitter: https://twitter.com/MathsTown Discord: http://discord.gg/wqayQhAT7W Grab a T-Shirt: https://amzn.to/3eIfqmX Website: https://www.maths.town ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $The Next Dimension - 3D Mandelbrot Fractal Zoom (MMY3D) Something a little different today! This video is a collaboration with fractal artist Yann Lby. This video projects the 2D Mandelbrot fractal into 3D using the iteration data for the vertical axis. It is rendered with Yanns own software MMY3D. Make sure you check out his amazing collection of 3D fractal zooms. https://www.youtube.com/watch?v=UoUDq1pkpOE&list=PL4lt5Vl4_TwrO3KDhVpp3_45DRZqtVNa- Please take the time to subscribe to Yanns channel, he has some great fractal content there (and tell him I sent you). Patreon Note: This video is not available for download on Patreon, because it contains the work of another artist. Rendered in 4k, from 8k data frames (at 30fps). The final magnification of this zoom is beyond e1000. More of Yanns work: https://www.youtube.com/watch?v=UoUDq1pkpOE&list=PL4lt5Vl4_TwrO3KDhVpp3_45DRZqtVNa- /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Discord: https://discord.gg/YphYVt787v Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Ko-Fi: https://ko-fi.com/mathstown (Buy me a coffee) ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/$ $Celtic Blue - Celtic Fractal Zoom (4k 60fps) A new fractal for you this week! This is the Celtic Fractal, a close relative of the Mandelbrot. In some ways it is part way between the Mandelbrot and Burning Ship. Many of the shapes youll see in this video are similar to the Mandelbrot, but it has islands and folds like the Burning Ship. A simple colouring this time, so that you can get the feel for the geometry of the fractal. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown Grab a T-Shirt: https://amzn.to/3eIfqmX ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ A Celtic Blessing - Bonnie Grace The Goths - Bonnie Grace Highland Hymn - Bonnie Grace Call the Herd - Bonnie Grace Re: -1.86056001606243046116884561224553816816388165211730248560683399811082332303275779654547124574808599402224206962237319969943598679965909574397031890550391447692502214277671092913724673260775907761 Im: -0.00000000000000000000000000000000000000000000000000000000000000094611788496797615857202737202017388521273816592809518865199967070723411203816986423212827992855122998898157600066567876123538400900 Zoom: 1.5095849699286317E169$

Deep in Thought - Mandelbrot Fractal Zoom (8k 60fps)

Classic 3 - 3rd Power Mandelbrot Fractal Zoom

$Classic 8 - 8th Power Mandelbrot Fractal Zoom Welcome to the Octobrot! Today we take a classic look at the 8th Power Mandelbrot fractal. A reversed (zooming out) version of this zoom is available for Patreons. Please subscribe! Thank-you to my supporters on Patreon. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/$ $Halloween 2021 - A Burning Ship Fractal Zoom I wasnt actually planning on making a Halloween video this year, but someone made a request in the comments. So here it is. An industrial flavour this year. Happy Halloween! Thank-you to my supporters on Patreon. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** OpenSea: https://opensea.io/collection/maths-town Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) Grab a T-Shirt: https://amzn.to/3eIfqmX Website: https://www.maths.town ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #Mandelbrot #fractal #mathstown #fractals$ $Infinity Liquid - A Mandelbrot Fractal Zoom Keep Calm, Drink Infinity Liquid!! With the world going crazy, perhaps some wild fractals is what you need to take your mind off things. You are going to need some serious bandwidth to watch this one, change your settings to at least 1440p, if not 4k, if your connection can manage it. This is the same technique I used for the Fractal Fluid video, but we explore a less dense are of the Mandelbrot Set here. Someone commented on that video they would like a 2 hours version, well here it is! Please subscribe. This video was made on my new PC using the brand new AMD Thredaripper 3990X (64-core / 128 thread) CPU. Around 70 hours of processing time was used to render this video. The magnifcation of the final frame is 1e1002 (Yes, that is 1 with 1002 zeros after it). Thank-you to my supporters on Patreon. There will be a 75mbs 4k version available for Patreons to download, but to be honest I could have made the bitrate even higher. /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Website: https://www.maths.town Twitter: https://twitter.com/MathsTown ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ Voice of the Sea - Bonnie Grace Deeper Than the Ocean - Bonnie Grace Neptune - Bonnie Grace Natures Wonders - Bonnie Grace Highland Hymn - Bonnie Grace Call the Herd - Bonnie Grace A Celtic Blessing - Bonnie Grace Tudor - Bonnie Grace The Norman Kings - Bonnie Grace The Goths - Bonnie Grace$ $The Land - A (Stretched) Burning Ship Fractal Zoom You are looking at the Burning Ship fractal, except it is very very stretched, skewed and rotated. Stretching certain areas of the Burning Ship reveals interesting Mandelbrot like features that have been hidden. Ive also used a bit of noise-based creative colouring in this one. This video is full of Earth colours. This video is running at half the usual speed because otherwise YouTube compression would destroy it. It is kind of relaxing this way though. Put this one on your TV and let it roll away in the background. If you like this kind of thing, then let me know. Thank-you to my supporters on Patreon. Ill have the high quality downloads available for you shortly. This video will be available for Patreons to download in the coming days, which will have a higher bitrate. You can also use these visuals on your own channel if you are a member of my Patreon page. https://www.patreon.com/mathstown /******************************************************************************** Patreon: https://www.patreon.com/mathstown (Support, Downloads & Usage Rights) Twitter: https://twitter.com/MathsTown Discord: https://discord.gg/YphYVt787v (Drop by and say hello) Grab a T-Shirt: https://amzn.to/3eIfqmX Website: https://www.maths.town ********************************************************************************/ Music from Epidemic Sound: https://www.epidemicsound.com/referral/ekoiev/ #BurningShip #fractal #mathstown #fractals$