diff --git a/content/blog/today-project/index.md b/content/blog/today-project/index.md new file mode 100644 index 0000000..8ce1b53 --- /dev/null +++ b/content/blog/today-project/index.md @@ -0,0 +1,82 @@ +Not too long ago I decided to create a pretty useless project. It shows emoji and color of the day. All of this is calculated by my formulas using my own algorithms on client-side. + +Here are some formulas that I used: + +* `t` - timestamp - const - 00:00 of this day in UTC. + +### Emojis: +The formula incorporates certain coefficients that are already substituted. The formula is not fully adapted. Some Unicode characters are missing, so I tried to find the longest consecutive sequences of emojis. + +* `tr` - `vector` - const - the start of emoji sequences (in Unicode). +* `ts` - `vector` - const - the difference between the numbers of the first and last elements in the sequences. +* `cet(t)` - a function used to calculate the sequence number of an emoji. +* `cev(t)` - a function used to calculate the decimal value of the emoji in Unicode. + +$$cet(t) = \left\lfloor 23 \cdot \left(3 \sqrt[3]{t} + 0.7 \cdot \log(t + 5) \cdot 13 + \frac{t \bmod 86400}{86400} + 11 \cdot \log_2(t) + 17 \cdot \sin\left(\frac{2 \pi t}{86400}\right) + 2 \cdot \cos\left(\frac{2 \pi t}{86400}\right) + \left\lfloor \frac{t}{86400} \right\rfloor^2\right) \right\rfloor \bmod 4$$ + +$$cev(t) = tr[cet(t)] + \left\lfloor 17 * (3 \cdot sin(2 * pi * t / o.7) + 5 * (3 \sqrt[3]{t} + 13 \cdot \log(t + 11)) \right\rfloor \bmod cet(t)$$ + +and is output looks like `&#{cev(t)};`. + +### Color: +Here, some cyclic operations are used, making it challenging to represent in a formulaic manner. I'll express it in pseudocode with a mix of mathematical formulas. This pseudocode may seem unconventional, but I am a genius, billionaire, and philanthropist. I have the complete right to use my algorithmic language if I am confident it will be understood by the reader (generally a mix of languages, but I believe it's quite evident). + +* `sv(t)` - a function used to fill an array (not implemented as a function). +* `cf(n)` - a function used to precalculate factorial (not implemented as a function). +* `num2permutation(k, n)` - a function used to determine the required permutation (from $n!$) of the sequence corresponding to number k in lexicographical order. + +``` +func sv(int t) -> vector { + vector el(3, 0); + + el[0] = t mod 1000; + el[1] = ⌊(t mod 1000000 - el[0]) / 1000⌋; + el[2] = ⌊(t - el[1] - el[0]) / 1000000⌋; + + return el; +} +``` + +``` +func cf(int n) -> vector { + vector factorials(n + 1, 1); + for i from 2 to n + 1 { + factorials.push(factorials[i - 1] * i); + } + + return factorials; +} +``` + +``` +func num2permutation(int k, int n) -> vector { + vector permutation(n, "0"); + vector was(n+1, false); + int cur_free, already_was; + + for i from 1 to n { + already_was = ⌊k / factorials[n - i]⌋; + k = k mod factorials[n - i]; + cur_free = 0; + + for j from 1 to n { + if was[j] is false: + cur_free += 1; + + if cur_free == already_was + 1: + permutation[i - 1] = (el[j - 1] mod 256) -> string; + was[j] = true; + } + } + + return permutation; +} +``` + +The color is output in the RGB format. + +--- + +*p.s. I feel that the task of finding the required permutation can be solved with a lower asymptotic complexity (`color.js`). If you have ideas, please write to me about it.* + +*p.s. [v2] I hate MathJax(((*