I am messing with julia sets currently and from each point I get a value of how many recursions until they escape the mandelbrot set. I can elaborate if needed.
Example from 0-4: (0,0,0),(255,0,0),(0,255,0),(0,0,255)
In essence, a function that makes a rainbow (based on RGB values) beginning with black, followed by red, and ending with blue for any defined length of the set.
I want to write down formulas in a very quick manner and have it ideally be visualized in a nice way during editing it. That’s why latex isn’t ideal although it is fairly quick and powerful.
Word has this quick formula editor that has all the functionality I need, but Word honestly doesn’t seem to be the right program. Ideally there is a program that lets me click together and formulate formulas in a natural manner, as if I was writing it manually. It could be a website or a program like dia is when it comes to graphs.
Use case: I will talk to somebody online and share my screen with him for teahcing purposes. (my handwriting is abysmal in paint 🙁 )
I am glad for any recommendations or ideas.
Here’s a simple concept: Any number that’s squared can be written as a series of sums of itself.
Example: 32 = 3 + 3 + 3 and 42 = 4 + 4 + 4 + 4
In the same way, the expression, x2 = x + x + x + … (x number of times)
Here’s what’s interesting, though. Take the derivative of both sides and you get: 2x = 1 + 1 + 1 + 1 … (x number of times). Now of course, 1 + 1 + 1 … (x number of times) is just x. So 2x = x? That doesn’t make sense.
I was thinking that the solution to this riddle is that you cannot take the derivative of a series which has a finite number of terms that is actually variable of the terms of the series itself. Is that the right intuition? Why else would this not work? Excited to hear your thoughts!
You have limited amount of tokens (for example – 100).
You can bet in the way that you choose your odds of winning or you choose the payout(multiplier of your bet) that you want to get. Both are connected so that if you set your odds of winning to 50%, the payout changes to what it would be with those odds in this game which is x1.98
The house (owner of the game) takes some percentage away from the total 100% so it has the edge, it’s 1% if i’m not wrong.
Betting: Maximum odds to choose are 98%, from which, if you win, you get x1.0102 of your bet and minimum odds to bet on are 0.01% and you get x9900 of your bet. For example if i set my odds of winning to 50%, then you would get x1.98 of your bet, but if i set that my payout should be x2, then the odds of winning would be 49.5%. The minimum bet amount is 0,0000001.
You roll a number between 0 and 9999 (both included).
You choose if you want to aim to hit lower or higher number.
For example if your odds for winning are set to 49.5%, then if you choose to aim for higher number, you would win if the rolled number would be higher than 5049, but if your odds for winning are set to 49.5% and you choose to aim for lower number, to win you would need to roll a number lower than 4950.
For example if your odds of winning are 98%, you would need to roll number greater than 199 if you aim to hit higher or less than 9800 if you aim to hit lower.
For example if your odds of winning are 0.01%, you would need to roll the number 0000 in order to win if you set to aim for lower and 9999 if you set to aim for higher.
With the limited amount of tokens I have, what is the best way to play to maximise my odds for profit and minimise my odds for losing at the same time?
If you have any questions, i’ll gladly answer them.
In secret Santa, each of the n people chose any of the other (n-1) people at random as their secret Santa. Any person choosing themselves is against the rules. The probability of the first person not choosing themselves is (n-1)/n. What is the probability that not one of the n people chooses themselves?
I’m talking from a first year university student perspective. If you just finished doing a cool problem, how often do you record the solution? I haven’t been doing that before now and I’ve found I can’t remember the problems I did just a month ago.
Any recommendations for apps (just got an iPad!) or ways to stay more organized (so far my course requires a ton of notes) ?
For context: In class yesterday, I was discussing a concept related to scaling images and getting real-world measures to my class. I spoke on how the real world has x and y representing directions and the image plane uses u and v.
My thought: Lately there seems to be an explosion of youtube videos (3blue1brown and major prep) that show us ways to use complex numbers to build intuition.
My question: Is there any significance to complex numbers describing an object on the image plane?
I’m trying to learn about the spectral theory of automorphic forms (reading Iwaneic). I think I would benefit from a source for some of the more basic complex analysis/spectral theory to reference as I go. I’d like to see derivations of the analytic continuoation/functional equation of zeta and gamma functions specifically, and potentially some of the Fredholm theory and theory of differential operators. I guess a source on complex analysis as it is used in number theory would be great. THanks in advance.