The Chaotic Cousin of the Mandelbrot Fractal

#shorts

Hi, welcome to my channel Absolutely Uniformly Confused, where I like to cover math topics that interest me. This video is about the Burning Ship fractal, which is a weird cousin of the Mandelbrot set where you take the absolute value of the components of z_n before squaring it. Despite this being a really unusual non-analytic map, the fractal ends up looking pretty cool in my opinion, if a little messy.

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[ervalance]

out of all the languages you chose to speak you spoke a fever dream

[andistansbury]

You're laughing. The ship is infinitely on fire and you're laughing.

[samuelwyatt]

"We flip it upside down because it looks better" is the most unexpected thing to hear in such dense video.

[anes-for-entertainment]

You're the most mathematician sounding mathematician i've ever heard

[majavmg]

When mathematicians mess with psychedelics.

[wizardsuth]

I once generated this fractal by accident when trying to render a Mandelbrot fractal. I made a mistake in the part that multiplies two complex numbers. It was cool enough I kept that version as well.

[Cup_TK]

Looks like a tear in the fabric of time

[arthur_agatapa]

i love how 10 minutes of vsauce explaining the imaginary axis in a paper made me hooked up into searching fractals for over 2 hours

[nostarswithoutdarkness]

This brings tears to my eyes. Truly incredible.

[theketchupboii]

Man i wish i could speak ancient latin tounge like this

[suspicioussand]

Advanced enough mathematics is indistinguishable from hieroglyphics really

[code_pi]

I've been wondering about this one for a while

[thestørmcrier]

I’m sorry I don’t understand or speak smart. Looks cool, that math though. That scared me

[exactspace]

I’ve definitely made it by chance just by changing things around with the Mandelbrot equation

[chumooskie]

Totally agree with this, the burning ship is my FAVORITE fractal by far and I need more of it

[johnchessant]

oh wow, that's cool. Basically half of the time (at each iteration) your number gets conjugated before being sent through the Mandelbrot function z^2+c. That must introduce a lot of "unpredictability" i.e. making it defy easy characterization

[amastelaire]

That's a crazy cool fractal. Nice video pretty interesting

[ZeroToMidnight]

Probably my favorite fractal. You can find some very cool things in it including a bunny and a human skull.

[danderamon]

When there is a beautiful and burning fractal: YO THAT IS SICK
the ship is burning it has fever and fever is a sickness

[blackholebusterisgood]

Fun fact I discovered about the burning ship: Instead of flipping the imaginary axis using the same equation for the burning ship, I discovered that replacing the adding imaginary number with a subtracting imaginary number (so it now looks like this: z=(|Re(z)|-i|Im(z)|)^2+c) flips the burning ship fractal in the same way without having to intervene with the grid