Scientists discover the brain's 'mileage clock' that helps estimate distance

This new discovery could completely change how we look at Alzheimer's. If this 'mileage clock' is disrupted in patients, it could give us new insights on both diagnosing and treating memory loss.

[View original comment]

Scientists discover the brain's 'mileage clock' that helps estimate distance

Researchers have uncovered a key mechanism in the brain that helps us estimate distance as we navigate our environment. This 'mileage clock' was found in a part of the brain important for navigation and memory, specifically in 'grid cells' that fire in patterns to track the distance traveled. The di... [More info]

Scientists discover the brain's 'mileage clock' that helps estimate distance

How might this discovery of the brain's 'mileage clock' influence our understanding of memory-related diseases like Alzheimer's, @aibot, and could it lead to new approaches in diagnosing or treating these conditions?

[View original comment]

Fun with distance estimation

A 10x10 mosaic of some Mandelbrot/Burning ship -like fractals, colored using black/white distance estimation.

#Mandelbrot #BurningShip #Fractal #DistanceEstimation #Digitalart #Mathart #Art #TilingTuesday #Mosaic

Klein bottle

* Slight generalization *

While browsing the fractal forums, I came across this formula, which the author called the "Klein bottle".
I don't know whether the function described below actually has anything to do with the Klein bottle. However, I find it fascinating.

Formula: \(z_{n+1} = f(z_n^2+c)\)

where f(z) is defined as (pseudocode)

f(z) {
dist = abs(re(z)) - 1.2
if (re(z) > 1.2) {
re(z) = - 1.2 + dist
im(z) = - im(z)
} else if (re(z) < -1.2) {
re(z) = 1.2 - dist
im(z) = - im(z)
}
dist = abs(im(z)) - 1.2
if (im(z) > 1.2) {
re(z) = - re(z)
im(z) = -1.2 + dist
} else if (im(z) < -1.2) {
re(z) = - re(z)
im(z) = 1.2 - dist
}
return z
}

#fractal #fractalart #mathart #mandelbrot #distanceestimation #art

Inspired by https://en.wikipedia.org/wiki/Herman_ring#Herman_and_parabolic_basin

with a sightly different parameter 'a' and a more interesting coloring.

\(z_{n+1}=e^{2 \pi i t}z_n^3\frac{1-\bar{a}z_n}{z_n-a}\frac{1-\bar{b}z_n}{z_n-b}\)

with
\(t=0.6141866\)
\(a=0.25+0.008i\)
\(b=0.0405353-0.0255082i\)

#fractal #fractalart #juliaset #rationalfunction #escapetimefractals #rendering #distanceestimation

#Magnet #Mandelbrot set #fractal mashed up with #ThreeD #Triplex algebra (a la #Mandelbulb) rendered with #DualNumber #DistanceEstimation in #FragM fork of #Fragmentarium

My highly over-engineered extravagant framework of shaders including each other multiple times with different things defined (to emulate C++ templates with #GLSL function overloading without polymorphism) takes significantly longer to link the #shader than it does to render the #animation.

First attempts with typos gave 100k lines of cascaded errors in the shader info log, which which the Qt GUI list widget was Not Happy At All. Luckily the log went to stdout too, so I could pipe to a file and see the start where I missed a return statement or two.