Skytopia

Love this - references one of my favorite ever optical experiences Eclipse of Titan https://www.skytopia.com/project/illusion/ipage-et.html

125ms is pretty bad though. In an online game that'd be borderline unacceptable lag... no local system should be THAT slow? Try it yourself here to see how bad that feels: https://www.skytopia.com/stuff/lag.html That page also links to a great video on what it's like on a touchscreen: https://www.youtube.com/watch?v=vOvQCPLkPt4

My favorite calculator is OpalCalc: https://www.skytopia.com/software/opalcalc/

I love SpeedCrunch, especially for dealing with different bases. For back-of-the-napkin type math, OpalCalc is my favorite. https://skytopia.com/software/opalcalc/

for Windows: OpalCalc more than nostalgic website but actively maintained: https://www.skytopia.com/software/opalcalc/ calcing with time is a bit jumpy at times, but other than that I love it for quick napkin calcing stuff costs 15 bucks

For Volumising Mandelbrot's Equation the Mandelbulb is worth a look: "In 2006 Daniel White inspired by an idea of Rudy Rucker developed a mathematical equation with the potential for a real 3D equivalent to the famous 2D mandelbrot set. With a modification by Paul Nylander in 2009 the Mandelbulb was born on fractalforums.com"[1][2] [1] http://www.fractalforums.com/still-frame/the-discovery-of-the-mandelbu… [2] http://www.skytopia.com/project/fractal/mandelbulb.html

Since you can burn out the receptors temporarily simply by viewing saturated color in the same place in your visual field for a while, you can just do this sort of thing: http://www.moillusions.com/2006/03/eclipse-of-mars-illusion.html Don't expect miracles of color, but it's sort of neat. This site claims to have more color variants, but these I haven't tried: http://www.skytopia.com/project/illusion/ipage-et.html Also, given the diversity of modern monitors and resolutions, you may need to hit CTRL-+ or CTRL-- a time or two for best effect

There are some amazing images of fractals on the web. One site that was pointed out here in particular was the Mandelbub, which looks amazing: http://www.skytopia.com/project/fractal/mandelbulb.html

These are three-dimensional slices made by varying certain parameters pertaining to the classic Z^2+C mandelbrot set. This is nothing new, except for varying the exponent, which indeed I had not seen before. Pretty pictures, though :) In the search for the "real" 3D mandelbrot, which recently lead to the discovery of the "Mandelbulb" fractal, the goal was to find a three-dimensional object with as much visual complexity as the classic Mandelbrot fractal, and which does not have mostly regions all stretched out like taffy. Especially the latter requirement is a problem with most "naive" representations of 3D Mandelbrot or Julia fractals. They're all stretched and skewed, and in some sense that's pretty, but it's a completely different type of "pretty" than the amazing spirals, flowerheads and branching lightning forks that are found in the classic 2D Mandelbrot and Julia sets. This is why people were so enthusiastic about the Mandelbulb fractal: Even though some regions of it were stretched and skewed like the previous attemps at 3D Mandelbrot fractals, there were also many, many regions that, for the first time actually did show three-dimensional romanesco broccoli flowers, organic spiral staircases and all sorts of amazing 3D visual complexity. And as described near the end of the (wonderful) essay on the Mandelbulb* it is not considered "the Real McCoy" 3D Mandelbrot set, not just because, as the author of this article implies, it is not mathematically elegant enough,…

> I simply don't buy the argument that the algorithms of cognition inherit any substantial amount of functionality from their physical implementation I'm somewhere in the middle on that. I wish for things biological to be clear-cut and deterministic enough that we can fully understand them the way we understand mechanical systems. But precisely because the brain is encoded in precious little DNA there is some evidence that there is more to it than meets the eye, after all if 50M of gzipped data can encode the whole thing why do we have such a hard time understanding it. There is enough repetition in there that some died-in-the-wool reverse engineer would have put 2 and 2 together by now if the secret was in the wiring or in some simple algorithm (ANNs for instance). Apparent order appearing from chaos is a field that has seen some study and the amount of complexity that can arise form simple starting data is quite amazing, witness the mandelbrot set and other fractal forms. It may be very hard to short-circuit such understanding and to 'divine' the workings of the formula without first going the long way around to understand the whole system rather than the 'seed' from which it grows. This is not simple mathematics where a simple equation on complex numbers gives you the mandelbrot set, it's possibly machinery interpreting an equation with 50 million terms. In different terms, given a very distorted (dissected) picture of the 3 dimensional mandelbrot set would you be…

Nice article, haven't seen this one yet! I was fortunate to be the first to render the Mandelbulb, there are some nice articles by the person who originally described the formula, Daniel White: https://www.skytopia.com/project/fractal/mandelbrot.html and https://www.skytopia.com/project/fractal/mandelbulb.html

http://www.skytopia.com/project/fractal/2mandelbulb.html This is the closest reference I could google. The article I am talking about had the author explain the various steps he went through, starting with rotating a 2d fractal, and move up the process to finally get the math equations to generate a truly 3d fractal.

Curious to see the 3D and 4D Mandelbrot using this method. Should look something like the last visualization on this page http://www.skytopia.com/project/fractal/mandelbrot.html but with more bulbs?

And for discussion of 3D analog of the original Mandelbrot, check out the Math Exchange discussion[1] and site dedicated to finding it.[2] The vanilla zoomed mandelbrot[3] looks 3d to me. It's interesting that actually turning them into true 3d is such an elusive problem. [1] http://math.stackexchange.com/questions/150117/is-a-3d-mandelbrot-esqu… [2] http://www.skytopia.com/project/fractal/2mandelbulb.html [3] http://www.skytopia.com/project/fractal/h-frac.jpg

There is OpalCalc for Windows: http://www.skytopia.com/software/opalcalc/

35.9% - look up sRGB for more info. (!00% of what a monitor can do, but 35.9% of what the human eye can see - especially greens are lacking.) Have a look: http://www.skytopia.com/project/illusion/2illusion.html

While not as clean or powerful as Soulver, OpalCalc looks quite interesting http://www.skytopia.com/software/opalcalc/

I really like the Soulver program that he mentions on the page for the "Scrubbing Calculator". I found a similar Windows/.NET program called OpalCalc: http://www.skytopia.com/software/opalcalc/ Time to do a web edition? Surely it already exists. Somebody help me out :P

Also note imaginary colors: http://en.wikipedia.org/wiki/Imaginary_colors You can see some imaginary colors here: http://www.skytopia.com/project/illusion/ipage-et.html

page 2: http://www.skytopia.com/project/fractal/2mandelbulb.html good link from page 2: http://www.bugman123.com/Hypercomplex/index.html

Unless cloud gaming company intend to put servers in every single city across the globe it's not going to work. Even in Boston with good, fiber internet streaming games have too much lag and the compression artifacts are horrible. When there is fast movement the compression is much more noticeable, worse then the lag. Many reviewers doing graphical comparisons do it with static images. It's quite common for the whole screen to become a blur of compressed and pixelated blocks at the slightest network hiccup. Also, you are misunderstanding what "reaction time of 100ms" means. It does not mean that any event that takes less time then 100ms imperceptible, it absolutely does not. The sound of a clap lasts 22ms and you are able to hear even shorter sounds. You can see light pulses of arbitrarily short length so long as they are bright enough. What 100ms reaction time means is that you can't react to a given stimulus in less then that. Here's the important distinction, you don't react to lag, you perceive it. To experience this for yourself, go this lag simulator webpage [1] and experiment with various lag times. You will quite easily be able to feel the difference in 0ms, 100ms, and 200ms of added latency. Keep in mind this is on top of whatever latency OS layers and browser sandboxing introduce. 1. https://www.skytopia.com/stuff/lag.html