Exploration of the 4D mandelbrot set on the Z-plane (Buddhabrot)

[YesIamJames]

Any way to render this as just a 3D shape? Possibly by rendering only at point 0 of the imaginary C axis. I just made my first buddhabrot renderer today but I don't have the skill to do it in 3D but I'd imagine you can get something just as beautiful as the Mandelbulb with some practice.

[albertlobo1981]

Awesome animation, great job! :D

[boinghd]

There were helix'. It makes me wonder if the universe is a deterministic system or not. I'm pretty sure that all the patterns that arise naturally would appear due to topological transformations of certain number sequences. It's interesting that we have complex numbers though. If we think of them in terms of natural processes, the fact that they even exist is a wonder.

[TiagoTiagoT]

Somtimes it looks like it is not a continuous volume but a bunch of cross-sections at different angles and depths put together; are those artifacts of the rendering or the actual numbers at full resolution really get distributed like that in some places?

[AluminumStudios]

@TiagoTiagoT Those aren't rendering artifacts. I cant explain it well because I'm not a mathematician, however what my software has revealed to me is that the fractal is actually thousands and thousands of Mandelbrot fractals, stacked on top each other, with each one twisting and tilting just a little bit into the various 4 dimensions. When viewed from just the right angle in all 4 dimensions they align and reveal the familiar Mandelbrot shape.  Interesting isn't it!

[ThePhysicsfreek]

My interest is in the projection of the MS in the quaternions in a 10 dimensional space/time. You have an interesting look. Really liked your imaging.

[DocFarnoff]

When I was introduced to the Mandelbrot by a TV special hosted by Arthur C. Clarke, my mind was completely blown! My life was changed.Everything had new meaning. I am a dunce when it comes to geometry but it look likes the Mandelbrot is a model of infinite dimensions not just four. One symbol representing a creator down to the smallest sub atomic particle and every variable in between!

[TheGodlyFoods]

AMAZING!



[funkyjj900]

look its Andromeda

[AluminumStudios]

@brendanharkness If you talk about our universe and the reality that we exist in, then the 4th dimension can be said to be time. But when dealing with mathematical constructs like this, a 4th dimension is just a 4th axis at a 90 degree angle to the X, Y, and Z axis. It is just a forth SPACIAL coordinate which defines the location of a point. It has nothing to do with time

[BoxOfStupidity]

@AluminumStudios I believe in the whole 4th spatial co-ordinate thing, but I realize that IF we say Time CAN be a spatial dimension, and a 4D object takes up multiple "spaces" of time, sort of how the 4th spatial dimension can be represented by multiple 3D Spaces, then maybe if the 4th dimension was time, and a 4D object occupied a multiple of spaces in "time" we see the slice that's in our moment? Idk, just seeing how i can relate the time one to the spatial one.

[AluminumStudios]

@BoxOfStupidity Interesting thoughts. I am not very well read on the topic, but I think many theorists consider time a dimension unto itself, different from space. I like to think of it this way - if you want to meet your friend, you must give them 4 coordinates. Ex." meet me on the 10th floor in the north-east corner of the building at 1:00pm." That is X,Y,Z, and time. Without the time coordinate you wouldn't be able to find your friend because you might go at the wrong time.

[BoxOfStupidity]

@AluminumStudios ah I never saw it like that!

[killthetaco]

@AluminumStudios how can there be an axis at a 90 degree angle to all x, y, and z? i can't visualize it, and if you just asume it to be true, than that means you would be adding 90 degrees so that...um... basic trigonometric functions become periodic not at every 360 degrees but at every 450 degrees (like scaling down the effect of every degree), and... and...... this is fucking with my mind, could you explain how you could have an axis perpendicular (would they still be?) to x, y, and z? thanks

[AluminumStudios]

@killthetaco More than 3 dimensions is not intuitive to our brains as we live in a 3D world. It is perfectly acceptable in mathematics however. A "tesseract" or "hypercube" is a 4D cube. If you google these terms you can find some animations, illustrations, and explanations that will help you understand. Also, in 4D, 360 deg. is all you still need to get the whole way around any one of the 4 axis :-)

[killthetaco]

@AluminumStudios i googled it and tried to understand it but it seems to be a little beyond me for now, but i feel excited!! i can't wait until i understand this stuff!! i feel like its going to immensely change my perspective in ways i can't imagine yet!!

[killthetaco]

@AluminumStudios

for now though, i have one more question. you say that this is "not intuitive to our brains as we live in a 3D world." is this based on something? a theory with backup? why is it that there are things that are simply impossible (if that is what you mean) for our brains to comprehend just because our environment does not have them? personally, i don't see why there should be any limits to our powers of understanding.

[AluminumStudios]

@killthetaco Our intuitive understanding is based on the fact that we only EXPERIENCE 3 spacial dimensions in our physical lives (there may be other dimensions according to string theory or depending on how you choose to define time, but despite that, we can't experience them.) Therefore, our brains really only process what front-back, up-down, left-right means. Trying to imagine another direction that is perpendicular to all o them is difficult to impossible.

[AntiProtonBoy]

Very pretty, nice work. Looks almost like Hubble pictures.

[petersrolo]

How can they be plotted if we only have the x y z axis. Is it plotted after being flattened to 3 dimensions? Wow this is confusing! Trying to understand a thing your brain cannot comprehend

[petersrolo]

4 dimensions?

[AluminumStudios]

@petersrolo Mathematically it has 4 dimensions. In our 3 dimensional world a point can be explained with 3 values - an x, y, and z location (left-right, up-down, forward-backwards) if you will. In the mandelbrot set, each point technically has 4 values which define it's location. These are the Real part of the initial "C" which was plugged into the equation Z=Z^2 + C, the Imaginary part of the initial "C", the Real part of the resultant "Z" and the Imaginary part of the resultant Z.

[AluminumStudios]

@petersrolo (reply part 2). This gives each point the values (Cr, Ci, Zr, Zi) to define it's location unlike our physical world where points have (x, y, z). It has four values and thus is said to be 4 dimensional. Our brains can't visualize 4 dimensions, so these values are projected (flatened if you will) down to 3 dimensions for this animation. It's not unlike looking at the shadow of a person. The person is 3 dimensional, but their shadow is 2D.

[quorumangelorum]

Wow.. this is stunning. The quintessence of beauty.