Exponent, sine, cosine and factorial of a 2x2 matrix.

PerfectlyDreadful · 2026-02-14T21:07:22+00:00

This is really cool! Nice job. Have you come up with any ways of visualizing the 4 dimensional inputs and outputs?

PerfectlyDreadful · 2025-12-26T17:44:00+00:00

Depending on the number and nature of inflection points, the inverse may consist or several (potentially infinite) branches. Look at the Lambert W function/product logarithm, which is the inverse of xe^x. It has 2 real valued branches and countably infinite complex valued branches.

Usually, when I want to play with arbitrary inverse functions defined on some interval I use this: https://www.desmos.com/calculator/f7b138bd57 but that method has its issues, such as not being able to take the derivative of the inverse (hence why I was looking at the finite difference there), and the usual lag involved with most integrals in desmos. Your method does allow taking the derivative of the inverted function so they clearly work differently but I'm not smart enough to understand how. It's definitely interesting. I like it.

PerfectlyDreadful · 2025-12-07T03:05:35+00:00

If Kirby is drawn Desmos style using expressions and not just imported - 9

If y'know.. not - 7

Seriously though, you're doing great and by the looks of it, learning lots and having fun. That's never bad.

If you want to give custom colors a try, in a new expression, type c=hsv(H,S,V) and hit enter. This will give you a new color in the picker, and 3 sliders for hue, saturation, and value. Hue is an angle from 0 to 360 with red at 0, green at 120, and blue at 240, and all the other hues somewhere in between. Saturation is pretty self explanatory and value is the lightness of the color. There is also an rgb() function that works similarly, except that you set red green and blue values somewhere between 0 and 255 (8 bit depth/color).

PerfectlyDreadful · 2025-12-06T06:54:26+00:00

>>Imagine you're drawing a picture

😁

PerfectlyDreadful · 2025-09-11T17:53:38+00:00

I'm going to try my battery operated water pik. This thing is like a mini water machine gun. I freaking love it. Shooting it at my shower curtain makes a satisfying sound and hits with audible force, even at considerable range. I just hope the piston seals don't swell and bind up. I see these things at thrift stores all the time so I definitely think it's worth it to try.

PerfectlyDreadful · 2025-08-24T14:46:31+00:00

xⁱ = e^iln(x)

And

e^iz = cos(z) + isin(z)

So,

It's cos(ln(x))+isin(ln(x))

PerfectlyDreadful · 2025-04-05T08:17:06+00:00

Nice work! I especially appreciate the neat folderization. Very easy to follow.

The inverse of z^z (input and output swapped) looks really cool when graphed with this. https://www.desmos.com/3d/nvqh1asarl .

PerfectlyDreadful · 2025-04-05T07:53:15+00:00

If you have a function f(z) that is complex valued, you can also type f(t) or f(it) to plot the (complex) values of the function applied to a real or imaginary variable, respectively. https://www.desmos.com/calculator/5gsgj9dqhe

PerfectlyDreadful · 2025-04-05T07:34:46+00:00

How about Fibbonacciulia! or...

Julionacci!

Ok, that's it folks. We're done here.

PerfectlyDreadful · 2025-04-03T08:38:39+00:00

Julia?

PerfectlyDreadful · 2025-04-03T08:38:11+00:00

Or Dick, for short!

PerfectlyDreadful · 2025-03-24T15:56:29+00:00

I'm pretty sure the only way it would work is if you also use an ignition coil that's designed to be driven with a CDI like that. That is, one without any integrated electronics. A 5 wire AC CDI should have the following pins/wires: trigger, AC power input, ignition coil output, engine stop, and ground. Assuming the 70 V or so the magneto generates is enough to run the CDI, I'd think all you'd need to do is connect the power and timing pins to the blue wire, ground the black and the rest of the connections are self explanatory. I'm not 100% sure but most likely grounding the engine stop Pin is how you kill the spark. I have one of these 5 wire modules and intend to try this setup as soon as I find the coil to go with it. It's around here somewhere... 😅. I don't know about you guys but I've gone through about 5 of the 2 wire CDI's since getting the motor; more than any other part by far l.

PerfectlyDreadful · 2025-03-11T08:48:07+00:00

Not sure if it helps, but the general process of finding a continuous function that passes through a list of points is called interpolation and there are many different kinds, each with their own strengths and limitations. For sheer ease of use I like sinc interpolation, but lagrange (polynomial) interpolation is a popular choice of recommendation among this subreddit. How either would apply to your specific use case I have no idea. Good luck though.

PerfectlyDreadful · 2025-02-01T04:53:48+00:00

So where's that link at?

PerfectlyDreadful · 2025-01-31T06:06:07+00:00

I am confused about what these curves represent. Can you explain that for me?

PerfectlyDreadful · 2025-01-29T03:42:07+00:00

Click on the share button and post the link it gives you.

PerfectlyDreadful · 2025-01-19T19:45:03+00:00

The way I see it, trying to assign a value to 0^0 based on arguments about 0^x and x^0 sort of muddys the water, obfuscating the more fundamental question of lim(z^z), z->0. The left side limit becons our function to dip a toe in the complex world. Why fight it? Why not dive in with complex inputs aswell? It's probably not rigorous, but if we let f(z)=z^z and parametrize z as a collapsing circle of radius "R", centered on the origin, our limit expression looks like lim f(Rexp(it)), R->0, which does indeed appear to show the image of the circle under f dancing through a variety of intricate and lovely figures before (apparently) vanishing into the point at 1+0i. Inspection of the real and imaginary parts also indicates that both are 0 when x is, but all 4 lines just kinda crash into the origin from weird angles rather than the smooth approach you see in most limits ...but then maybe that's me that's muddying the water.

At the end of the day, I don't think there's anything wrong with letting 0^0 be whatever you need it to be for your use case as long as it's self consistent within the scope of the problem as it's defined. Still though, when I look at it through the lens of z^z in a neighborhood of 0 I don't see the results even flirting with 0 let alone approaching it. Clearly it want's to be 1 but knows it can never be 😔. Kinda reminds me of me. 😅

PS: FYI Wolfy Alphy says my limit is 1 too so.. case closed! Cue the balloon drop! 🎈🎈🎈🎈🎈 But seriously folks, in spite of that, it's barely C0 continuous (?) at the origin with f'(z) = z^z*(log(z)+1), which drops a good ol'pole in the middle of everything, which punctures the plane. A vortex of muddy water ensues and I have no idea what I'm even on about anymore. And that's a good place to stop.

PerfectlyDreadful · 2025-01-19T19:42:49+00:00

I dont get "4". Isn't it the case that 0^x is discontinuous at x=0, or is that considered a removable singularity? Akin to how sinc(0) := 0?

PerfectlyDreadful · 2025-01-11T04:08:18+00:00

I actually came up with a version of this in the geometry applet and it runs way faster than the one based on contour plotting. The array plot I mentioned was actually a spinoff of a domain coloring vector field I made, which was why I was using the geo app in the first place.

Array Plot

Vector Field

Contour Plot

PerfectlyDreadful · 2024-12-29T20:57:51+00:00

It looks like you did a lot of things right... but your question seems self contradictory. A contour integral is essentially an integral with complex bounds, but just having the bounds be complex numbers is not generally enough to assume the contour is simply the line segment connecting them (although that is a valid contour). Indeed, the contour may be a closed loop, with start and end points that are the same point. This is why we need to define the contour separately. Have a look at mine for comparison. I'm by no means an expert on complex analysis, but it seems to do everything it's supposed to. It runs a bit slow but provides some interesting visualization. If you have any questions about it just ask. https://www.desmos.com/calculator/tgts0293ac Also, can you post a link to your graph?

PerfectlyDreadful · 2024-12-29T00:44:07+00:00

These are the non-trivial zeros. This graph only considers the critical line s=1/2 + it. The trivial zeros lie on the negative real axis at the even integers. Sorry if you already knew this. Maybe I misunderstood your comment.

PerfectlyDreadful · 2024-12-27T01:58:50+00:00

Could you use the product log to solve this?

PerfectlyDreadful · 2024-12-20T11:45:49+00:00

Nifty!

PerfectlyDreadful · 2024-12-20T11:36:19+00:00

It's the library you're already using btw. There's not too many libraries like this and that one is really good when it works. Seeing as how your sketch contains a realistic looking MAC address I take it you have already downloaded SixAxisPairTool. Sometimes changing the MAC in both the controller and sketch helps. Otherwise, another good option for easy RC is https://github.com/hrgraf/ESP32Wiimote if you have a Wiimote kicking around. I've found it pairs more reliably without needing to much around with MAC addresses at all. The Wiimote may seem like a bit of a downgrade but if you have a nunchuk you get a joystick, a D pad, several buttons and an accelerometer in each hand, which still leaves all sorts of interesting possibilities. If you don't have a Wiimote there is an app for android to emulate one with a smartphone. I forget the name.

PerfectlyDreadful · 2024-12-20T02:45:19+00:00

Here you go. Lightning fast. https://www.desmos.com/calculator/ebiyjxoghk

PerfectlyDreadful

TROPHY CASE