Yesterday i learned about the chaos game. To the the thing in real life, when i grew tired of drawing and measuring points in paper and rolling a die, i programmed it on python.
then i asked myself what would happen if i tried the same thing with 4 "corners" instead of 3. keep in mind, the corners were still placed randomly, never creating a perfect square, just a quadrilateral.
and the fractal pattern was still there. although it had like "noise" on some triangular shaped areas, getting just random points on those.
then i checked the wikipedia page on chaos game https://en.wikipedia.org/wiki/Chaos_game and it said there that if you try to use the same rules from the triangle but for a perfect square (or a normal square, i guess they are always perfect), it just creates random noise, no pattern appears.
i tried it with a third program and yes, if the four corners are situated at the beggining NOT at random but forming a true square, you get nothing.
So my question is...why is it that when you do it with 4 corners but not in a perfect square shape, the pattern appears but when its regular, the pattern does not appear? is there a specific point of "regularity" when the pattern dissapears? and also, i've noticed that when the pattern appears, there is a triangular area where points are random noise. why is it triangular? and does its area/shape/placement have some relation to the "triangle" that it could be if there were only 3 points?
ill add access to the three programs in python if you want to try them for yourselves or read the code
https://github.com/juanmata42/Sierpi-ski-question
inside:
Sierpiński_triangle.py creates the triangle with the chaos game
prueba cuadrilatero aleatorio.pystill with random "corners" but having 4 of them. here the pattern appears
fractal cuadrado.pyhere the square is perfect and the pattern does not appear
https://preview.redd.it/2h4n3qpropg51.jpg?width=334&format=pjpg&auto=webp&s=cf9f87f666aabfc26788830b1c4630721aaff95b
I was reading Neville Goddard scholar and historian, Mitch Horowitz’s book, “The Miracle Club” and got a book suggestion for a new book “Scripting the Life You Want: Manifest Your Dreams with Just Pen and Paper” By Royce Christyn.
In the book Christyn explains how he developed his scripting method through four years of trial and error, keeping what worked and dropping what didn’t until he brought his success rate from 5% to nearly 100%. An interesting part of the book outlines some relatively unknown scientific discoveries and emerging technologies.
Creation is Finished
In the Foreword, Horowitz mentions:
“There is a brick-by-brick realism to Royce’s approach . . . and something more. In my years as a seeker and writer within New Thought, I have come to feel that we do not manifest events. I believe, rather, that amid varying laws and forces under which we must live, we are able, through perspective, focus, mental pictures, and emotionalized thoughts, to select events from a nonlinear field of infinitude. I develop this theory in my book The Miracle Club, and I won’t get into the weeds of it here. Suffice it to say, certain finely crafted and practicable exercises help us enter that field of selection. Some exercises work better than others, employing and engaging our psyches in the most productive ways. What you are about to experience is, in my view, one of those rare and remarkably effective methods that help galvanize your mental and emotional forces for maximum potency and results.”
That we “select events from a nonlinear field of infinitude” echos Neville Goddard’s famous words “creation is finished.”
In Neville’s “Five Lessons: A Master Class” (1948), he says:
“As we told you last night, you have but one gift that is truly yours to give, and that is yourself. There is no other gift; you must press it out of yourself by an appropriation. It is there within you now for creation is finished. There is nothing to be that is not now. There is nothing to be cre
... keep reading on reddit ➡
Hi all.
I am struggling to get a sierpinski triangle to render properly in 3D. I am loosely basing this off of this: http://blog.hvidtfeldts.net/index.php/2011/08/distance-estimated-3d-fractals-iii-folding-space/
I have tried various different methods of drawing the sierpinski triangles, but it seems to only draw the vertices where it's located, rather than edges or faces. I must be missing something, as trying to draw the sphere or even any other object here I have no problem.
Here is an example of how I'm drawing this (in Unity3D): https://gist.github.com/beckerej/e9a50360999557a35aeb17f26b8b65c0 . This just includes the relevant parts, so it won't compile.
Here's what the output is looking like: https://i.imgur.com/OPbI38Z.png (with no shading, just normals)
I would love for some insight on what I'm doing differently than these examples:
https://www.shadertoy.com/view/Xd2XDW
https://www.shadertoy.com/view/XdVGDt
Thanks!
Has anyone used the Sierpiński triangle or other fractal as an antenna design? If it were setup correctly it may be able to be very sensitive to matching frequency lengths. Thoughts?
So if you have a Sierpiński triangle with a scaling factor of 2 and is self-similar into 3 parts, the dimension should be log(3) / log(2), which is approximately equal to 1.58. Have you heard of this before as well?
While being bored i made a redstone Sierpiński triangle plotter so here it is : This picture is it from the from it spanes from bedrock to max build height https://imgur.com/A6AB5zh and this is the redstone https://imgur.com/zymASXt https://imgur.com/3PZSedc
If you have any questions i would be happy to answere
The universe is built around symmetries. They express themselves in nature on both macroscopic, as well as microscopic scales. They tell us about the nature of patterns in objects and the interactions that occur among particles.
The Golden ratio, The Fibonacci sequence and Fractal patterns are such three elegant concepts that underlie the design of the universe.
An exciting idea some scientists posit is Emergence Theory, which attempts to unify General Relativity and Quantum Gravity under a unified framework. At its core, Emergence Theory employs the ideas of Golden Ratio, Fibonacci Series and Information theory. The entire creation of the universe can be visualized as a profound simulation built primarily from bits of information. From it to bit. This is an idea supported by Digital Physics and The Simulation Hypothesis. Likewise, computer generated patterns like the Sierpiński Triangle, a fractal structure that emerges from simple rules, and Barnsley's fern, and bifurcations in the logistic map are all hinting at the symmetrical nature of the Universe.
In fact, the Golden ratio also appears in Cosmology as well in Black Holes where temperature changes from positive to negative. The equations governing the lower bound on Black Hole entropy also include the Golden Ratio or “Phi” and it is also conjectured that loop quantum gravity can also be related to black hole entropy via the Golden Ratio. Even Spiral Galaxies like our Milky Way follow the Fibonacci Sequence.
The case is no different in living beings, the Golden ratio is expressed in the design of the face. The position and distance between the mouth, nose, eyes, ears and chin all follow the Golden ratio. A person’s body will appear to be more symmetric if his/her proportions of different parts of the body adhere to the Golden Ratio.
Noether’s theorem, a theory with profound insights on the nature of symmetry, basically states that any symmetry in nature has a corresponding conserved quantity. Einstein’s theories of General and Special Relativity also give rise to a fundamental symmetry between space-time and mass-energy. The gauge symmetry transformation of particles. To put it simply, nature is built around symmetries.
There are even certain patterns in nature that recur across different scales. The spherical organization of cells in an embryo, the arrangement of petals in a flower, the spots and stripes on the bodies of a cheetah and zebra etc. all show such a type of pattern recurrence
... keep reading on reddit ➡I spent a day farming/gardening yesterday. I got really tired after dinner, which I expected. By 7pm, I was laying paralyzed on my bed, having way more profound hallucinations than I ever had on shrooms (I’ve taken fives times in life) or LSD (I’ve taken that only once in life). I was being shown so many cute, but strange creatures. Geometry patterns up the ying yang, and unidentifiable organic motifs. At one point, a Sierpiński triangle, who was a living being, began moving like a 5-D object, and opening up to let me enter inside of it. From inside it became a 5-D-360 fractal geometry show. I used to do salvia about a decade ago with my cousins regularly on the weekends, and that is the best comparison to describe this episode, except this lasted from about 7pm to 1am. At 1 am, I got up, still tripping hard, and went to actual sleep. I got up normally, but very groggy, and having issues “integrating” back into the world and my school work. For hours, if I closed my eyes I had strong visual hallucinations of psychedelic scenes. It took me all day to “get my head straight”. I had to do stats homework in this condition. Also, as intense as the initial trip was, I was never scared, in fact I was happy and entertained during this entire “ride in the Fractal Triangle”. I hadn’t taken any psychedelics since Halloween, so...what happened to me? I have strong doubts it was a dream. I’m a vivid dreamer, but this was a full-emersion trip, not a dream. I’ve never needed a whole day to shake a dream off. Did I have a flashback of some sort?
If you want to receive this as a daily email in your inbox, you can now join at this link
r/worldnews
Judge refuses to name fame-craving 'incel' killer as she convicts him of 10 murders:
Bolsonaro tells Brazilians to ‘stop whining’ after record Covid-19 deaths
Scotland would ‘fare better’ outside the UK, more than two thirds of Scots say
r/news
Bucking GOP trend, Alabama governor extends mask order
The United States is now averaging 2 million vaccine doses administered per day.
Fauci calls loosening Covid-19 restrictions inexplicable as variants threaten another surge
r/science
**We daydream as children, but hardly do it as adults, even thought it may boost wellness and pain tolerance
... keep reading on reddit ➡Phil
Sudden Lee
Go post NSFW jokes somewhere else. If I can't tell my kids this joke, then it is not a DAD JOKE.
If you feel it's appropriate to share NSFW jokes with your kids, that's on you. But a real, true dad joke should work for anyone's kid.
Mods... If you exist... Please, stop this madness. Rule #6 should simply not allow NSFW or (wtf) NSFL tags. Also, remember that MINORS browse this subreddit too? Why put that in rule #6, then allow NSFW???
Please consider changing rule #6. I love this sub, but the recent influx of NSFW tagged posts that get all the upvotes, just seem wrong when there are good solid DAD jokes being overlooked because of them.
Thank you,
A Dad.
Because a toothbrush works better
So far nobody has given me a straight answer
Had to ground him until he could conduct himself properly.
I am currently in the hospital. I had a back operation yesterday. The surgical nurse came in my room and started asking questions about my back. She asked me if I had any falls during the last year. I responded just one. It was after summer.
She laughed and said in 20 years of doing this she never was told that joke.
Indian places are naan profit, Vietnamese places are pho profit.
..... Will get a reward.
