Fractals are typically not self-similar

When something is referred to as fractal, does it always imply a degree of self-similarity? As I understand it, Mandelbrot developed fractal geometry as a tool to examine the "roughness" of reality as opposed to the smoothness of calculus and fractal dimension is a measure of complexity at every scale, with a self-similar pattern being an easy example to follow. If that is so, that the universe has a high degree of complexity at every scale, is that really controversial? Here is an excellent 20 min introduction to fractals: ▶ this video

in “The Hindu Temple as a Model of Fractal Cosmology (2015)” · View on HN

There is a common misconception, repeated here, that fractals are defined by their self-similarity. This is not true. Fractals are mathematical objects which have non-integral dimensionalities: that is, they exist in a space somewhere between (n)D space and (n+1)D space for some integer n .[1] The exact Hausdorff dimension, the number quantifying their dimensionality, is not in general the same for each construction. For the Koch curve, the Hausdorff dimension is ln(4)/ln(3) = log_3(4) approximately 1.2619.[2] This is because for each iteration of the curve's construction, the perimeter of the curve grows by a factor of 4 while the area enclosed by the curve only grows by a factor of 3. That makes it fill space faster than a growing 1D line, but slower than a growing 2D surface. [1] ▶ this video [2] [link]

in “Recursion and Fractals” · View on HN

"Perhaps calling it a fractal is an unnecessary spin," It is, or at least calling it self-similar is, as well as what the image implies: ▶ this video That's a 3Blue1Brown video explaining why "fractal" and "self-similar" are not the same thing.

in “Could 'Oumuamua be an icy fractal aggregate ejected from a protoplanetary disk?” · View on HN

"Would people consider a colour photograph as encoding four dimensional information when its pixels are represented as (x, y, brightness, colour) for example?" Actually, yes, they do. Computer vision people will envision a photograph as containing the number of dimensions equal to the number of independent numbers used to describe it, so a 1000x1000 RGB image would be considered 3,000,000-dimensional. This is perfectly routine in that world. Writing would be considered n-dimensional. [link] In non-math terms you'd probably be justified in saying the question is ill-defined, as what constitutes an orthogonal vector component in a piece of writing is not something that has an universally-obvious answer. But it's not that there are 0 possibilities, it is that there is very many. In a nutshell, the word "dimension" does not simply describe 3-dimensional space, and all other uses are somehow wrong. Dimension applies to any independent element of a vector, and using it to describe spacetime is a tiny, tiny subset of the valid uses of the term. Another very common example is that describing the movement of a free floating in space rigid body is a twelve dimensional value; you need to describe x, y, and z (or equivalant), you need to describe the rotation around x, y, and z, and then you need to describe the velocity of each of those components. That's 12 dimensions. In fact, it's 12 dreadfully mundane dimensions. Incidentally, not included in valid uses of the term is the sci-fi sen

in “The special data device SpaceX’s Falcon Heavy sent to orbit is just the start” · View on HN

I am unable to answer your questions for you, but I wanted to talk on the topic because it is something I've been thinking a lot about lately There recently was a lot of talk and reporting surrounding YouTube 'changing their algorithm' and hurting a lot of YouTubers I watch frequently One of my thoughts was that unfortunately the best solution would probably mean content creators would need to seek their own advertising'sponsorships I can tell you the only ads I have clicked on in any recent memory are all, every single ad, of the ones that 3blue1brown places at the end of thaer videos(o) Considerate effort like this really made me think how inconsiderate and detrimental the current hands off one size fits all ad networks are Some content creators will surely protest 'im a creator stead a salesman' which is a fair complaint but I'd argue 3blue1brown really brings an artistry to the personal ad network the channel is creating.. self curated ads has the potential to be another medium of self expression (o) [link] .. an aside: the ad that YouTube ran in front of the video I linked when I first clicked on it was offensive and jarring, it depicted an animated Albert Einstein literally scribbling on a black board while a student looked on in dread and three words came in the screen, two of which I can remember 'math ___ sucks' the middle was either: teachers, lessons, or tutors; this ad actually upset me.. contrast that with this great 3blue1brown ad(i) and I am more confident in m

in “Ask HN: Anyone monetizing their sideproject with direct ads / sponsorships?” · View on HN