When i was a child, i was thinking what would come beyond smallest, and what comes beyond biggest. It was then i realised. Infinite has always been a circle, a cycle of infinite causality. After the biggest, comes the smallest and before the smallest comes the biggest. Before birth, comes death and after death comes birth. Finity originates from the limited perception of mortality, so only time creates limits. This was when i started to ask me a question for years. The time before my birth, is it the time after my death? Unexistence. Absence. Unperceivable. *it will never end, it has never begun*
Some areas of the Mandelbrot set have nicknames. One is often called seahorse (or seahorse valley for the region where those are). When viewed as an elevation map, that place seemed more like a shoreline to me. So seahorse coast, or abbreviated just horse coast.
@@Life_42 yep(agreeing with your rebuttal). Though people do speculate if there are fractal dimensions through which the particles of existence emerge and re-emerge over infinitely long time scales.
I like what you've done there, trying to work out how! I use mandelbulber in my YT fractals. If using that I think you get get something like you've done using a bounding box but I like the model, it like a cliff-line on the coast - liked 👍
I guess the number of iterations until z <= 2 is just mapped to height dimension z and then rendered as 3d together with the real and imaginary dimensions x and y.
Hey, i don't why i got this recommended but looks nice, It'll be great if the "camera" position will more in the center of the plane(literally zoom in), this way when the plane rotates you're surrounded by the wonderful fractal field, barely seeing its limits creates a more immerse experience. Bonus track include some trippy music.
Usually with a Mandelbrot fractal, a simple computation is repeated until the result satisfies some condition. The number of iterations until that point is often called "escape time". Such a calculation is done per pixel and we end up with an array of these escape times. Usually those pixel values are then used to look up a color in some (aesthetically prepared) color palette. Here I use those values as an elevation above ground level (after some more tweaks with a mapping function from escape time to elevation, to better control slope and other details of the appearance).
Is life part of a higher dimensional fractal? From the planck size to the size of the observable universe, makes me wonder how much smaller and larger it goes.
I have this image in my brain of a scientist peering into a microscope, gradually zooming in further and further, from the cellular level to the molecular, then the atomic, quantum, whatever, until eventually he's peering down into the Big Bang, the Milky Way, the Solar System, and down to the back of his own head
There is a lake of peace and tranquility, they say. It lies in the middle of the mountains, where foolish wanderers can get ensnared by the slightest difference in a decimal place, trapped in endless, mesmerizing patterns.
I can confirm that one can get lost there, always looking for something. "I'll recognize it when I see it", I keep telling myself. But instead I stumble over more unexpected surprises again and again. I should probably go out more. 🙂
I wrote my own programs. They aren't really usable by innocent bystanders; instead of designing a proper user interface, I just tweak the source code and keep recompiling.
There is an old philosophical quarrel: is math invented or is it discovered? I am among those who believe math is discovered, and so I also believe that math is something natural, not something artificial. It may sound strange to see me write that when I am programming a computer to produce abstract vistas. But the natural origin of math doesn't preclude it from being used for artificial constructions, too. That is simply what we call technology: making use of the laws of nature for our own purposes.
I don't use raymarching. In fact, I am not rendering the mandelbrot mountains directly. There are two distinct pieces of software. The first program is a Mandelbrot zoomer with arbitrary precision arithmetic, and it can output iteration data in addition to colors. The second program is a heightfield renderer. It receives the iteration data as raw elevation map, not knowing that it was generated from a fractal formula. Both programs do their specialized task quite "traditionally", with no truly novel algorithms. There are additional details, for example I start from smoothed iterations ("continuous escape time", or "renormalized itrations", but any variant will work). Then I have to apply a special non-linear mapping to the iteration data to make the overall slopes more interesting. Something along the lines of exp(-iteration[pixel]/maxiter), because otherwise the height maps are simultaneously too flat and too steep.
This one is not a mesh. It was made with the "Persistence of Vision" Raytracer ("povray"). That's a fairly ancient piece of software, from before everyone settled on triangles as the one true surface primitive. The noodle is made from torus pieces (i.e. donut rings). Povray can render toruses, quadric surfaces and many other types of such "algebraic surfaces" directly, without tesselating them into meshes.
@@procedupixel213 I see. Amazing, I remember POVRAY from a long time ago. I heard of it being quite different, but I always thought it still used tessellated meshes.
@@sjoerdevIt's not as masterful as you'd like. There is no user interface, it's convoluted, and the algorithm really needs a rework for more speed. Just not the kind of thing anybody could feel good releasing to unsuspecting bystanders. 🙂
An older version of my height field renderer might still be available on fractalforums.org, where I used to be a regular before I overstayed my welcome.
Notice that points at the same height all have the same colour, so I'd guess that there really isn't anything fancy going on - they're probably just rendering each point's escape time as a corresponding height and colour, while the normal Mandelbrot just renders colour
