So Nota didn’t have plot support before. But I did have very nice charts in Intactus . So I thought lets add it to Nota , but way better… And by way better I meant compact and rendered way way better. Then I also added the functions for getting the digits of a number as matrices (integers and decimals) and with that you can do these things. like the diff of digits of pi and e. Nota has become such a rich language.
So trying to see what you can do with Nota Language now, I computed the first one hundred Fibonacci numbers, and then got their first digit and plotted them. I also made the charts to have rounded characters which makes them render way more nicely, and fixed so many problems in Nota including many things that results in panics, This is just amazing, but what you can do with Nota these days, and the pattern itself.
You know that I had added Nota Language support to Archive , but it was rendering of math, never executing Nota Code . I thought… Why not? And so with some modification in the Nota side and Archive side, this now works quite amazingly. The rest of the things you’re reading, I only wrote the code for them, and in the building phase of Archive , they got executed into numbers, matrices, and the charts that you see. Quite fun right? It is like reading a Maestro Wolfram writing with its embedded Wolfram Language code. Now I have that as well. So with a few examples, let me show it to you…
Fibonacci is a fascinating sequence. You start with [1, 1] then add up the previous two numbers together:
In Nota Language , this can be written in recursive mathematical form:
And it also can be expressed through the loop mechanism which lets you write to a result variable iteratively (this is the non-standard feature of the Nota compared to math, and it breaks math’s static-ness). I added it because I wanted to see what happens in the ecosystem of math if you have something like this, and it is fun.
But then there is a very interesting formula by Jacques Philippe Marie Binet. I found it around when I was a freshman at the high school, our teacher said “there is no formula for Fibonacci” (idiot) and so I found this and won a bet:
Now lets have a tool to get the first digit of some numbers:
By having this tools. Now lets do something really cool. Lets see how the first digits of the Fibonacci sequence looks like
This is something amazing. If we look at the raw numbers, they themselves somehow represent the series.
This is either very new to you, or very old. My whole point was to show you executable Nota inside of the Archive :) And then there are many other interesting things that you can do. Like the one in the photographs, lets compute the delta of pi and e’s digits:
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![In[1]: Digits[x] = plot[decimals[x, 100], 10]
Out[1]: 0
In[2]: 𝛱 = Digits[π]
┌─────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ ┌┐ ┌┐┌┐ ┌┐ ┌┐ ┌┐┌─┐ ┌┐ ┌┐ ┌┐ ┌─┐ ┌┐│
│ ││ ┌┘│││ ┌┐ ┌┐ ││ ┌─┐ ││ │││ │ ┌┐ ││ ││ ││ ┌┐ ┌┐ ┌┘ └┐ ┌┐ ┌┐ │││
│ ││ │ └┘│ ││ ││ ┌┘│ │ │ │└┐ │││ │┌┐ ││ │└┐││ ││ ┌┘│ ││ │ │ ││ ││ ┌┐ ┌┘││
│ ││┌┐ │ │ ││┌┐┌┐ ││ │ │ │ │ │ │┌┘││ │││ ││ │ │││ ││ │ │┌┐ ┌┐│└┐ │ └┐││ ││ ││┌┘ ││
│ ┌┘││└┐┌┘ │ ││││││ ││ │ └┐ │ │ │ ││ ││ ││└┐ ┌┘│ │ │││ ┌┘│ │ │││ │││ │ │ │││ ││┌┐ │││ ││
Out[2]: │ │ ││ ││ │ ││││││ ││ │ │ │ │ │ ││ ││ ││ │ │ │ │ │││ │ │ │ │││ │││ │ │ │││ ││││ │││ ││
│ ┌┐│ ││ ││ │ │└┘││└┐ ││ │ │ │ └┐│ ││ ││ ││ │ │ │ │ └┘└─┘ │ │ ││└┐│││ │ │ │││ ┌┘│││┌┐ │││ ││
│ │││ ││ └┘ └┐┌┘ ││ └─┘└┐│ │ │ ││ ││ └┘ └┘ │ │ │ │ │┌┐│ ││ ││││ │ │ │││┌┘ ││└┘│ │││ ││
│ │││ └┘ └┘ └┘ └┘ │┌┘ ││ ││ │ │ └┐│ └┘││ ││ ││└┘ └┐│ └┘││ └┘ └┐ │││ ││
│┌┘└┘ ││ └┘ └┘ └┐│ ││ ││ └┘ ││ ││ ││ └─┘││ ││
└┴──────────────────────────────┴┴────────────────┴┴──┴┴─────────┴┴────┴┴────┴┴──────┴┴──────────┴┴──┴┘
In[3]: E = Digits[e]
┌─────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ ┌┐ ┌┐ ┌┐ ┌──┐┌┐ ┌┐ ┌┐ ┌┐ │
│ ┌┐┌┐┌┐┌┐ ││ ┌┐ ││ ││ │ │││ ││ ││ ││ ┌┐ ┌┐ │
│┌┐││││││││ ││ │└┐┌┐ │└─┐┌┐ ┌┐││ │ │││┌┐││ ││┌┐ ┌─┐ ┌┐ ┌┐││ ┌┐ ││ ┌┘│ ┌┐ │
│││││││││││ ││ ┌┐ │ │││ ┌─┐ │ │││ ││││┌┘ ││││││└─┘└┘└┐│ │ │└─┐ ││││ ││ ││ │ │ ┌─┐ ││ │
│││││││││││┌┘│ ┌┐ ┌┐││ │ │││ ┌┐│ │ │ └┘│ │││││ └┘└┘││ ││ │ │ │ ┌┐┌┐│└┘│┌┘│ ││ │ └┐┌┐│ │ ││ │
Out[3]: ││││││││││││ │ ││ ││││ │ │││ │││ │ │ │ │││││ ││ ││ │ │ │ │││││ ││ │ ││ │ ││││ │ ││ │
││││││││││└┘ │┌┘│ ││││ │ └┘│ │││ │┌┘ │┌┘││││ └┘ ││ │┌┐│ │ │││└┘ └┘ │ ││ │ ││││ └┐│└┐│
││││││││││ ││ │┌┘└┘│ │ │┌┘││ ││ ││ ││└┘ ││ ││││ └┐┌┘└┘ │┌┘│ │ ││││ ││ ││
││││└┘││└┘ ││ └┘ │┌┘ ││ └┘ └┘ └┘ ││ └┘ └┘││ ││ ││ └┐│ └┘││ └┘ ││
││└┘ └┘ ││ ││ └┘ ││ ││ ││ └┘ └┘ └┘ ││
└┴───────────┴┴──────┴┴────────────────────┴┴──────────────────────┴┴───┴┴───────────────────────────┴┘
╭ ⎡ ⎢ ⎤ ╮
In[4]: 𝛥 = plot│ ⎢ integers[x] ⎢ x ∈ |𝛱 - E| ⎥, 10 │
╰ ⎣ 1,1 ⎢ ⎦ ╯
┌─────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ ┌┐ ┌┐ │
│ ┌┐ ┌┐ ┌┐ ││ ┌┐ ││ ┌┐ ┌┐ │
│┌┐││ ││ ││┌┐ ┌┐ ┌┐ ││ ││ │└┐ ┌┐ ││ ││ │
│││││ ││ ││││ ││ ││ ││ ││ │ │ ││ ││ ││ │
│││││ ┌┐ │└┐ ││││ ││ ││ │└┐ ┌┐ │└┐ │ │ ││ ┌┘│┌┐│└┐ ┌┐ ┌┐│
Out[4]: │││││ ││ │ │ ┌──┐ ││││┌┐ │└┐ ││ ┌┘ └┐│└┐ │ └┐ │ │ ││ ┌┐┌┐┌┐│ ││││ │ ││┌─┐│││
││└┘└┐ ┌┘│┌┐│ │ ┌┐ │ │ ││││││┌┘ │ ┌┐│└┐│ └┘ │ ┌┐│ │┌┘ │ ┌┘│┌──┘││││││ └┘││ └┐ ┌┐│││ ││││
││ │ ┌┘ ││││ └┐ ││ ┌┘ │ ┌┐┌┘││││││ │ ┌─┘││ └┘ │ ┌┐┌┘││ └┘ │┌┘ ││ ││││││ └┘ └─┘││││ ││││
││ │ │ ││││ │ ││ │ │ │││ ││││││ │ │ ││ │ │││ ││ ││ ││ ││││││ ││││ ││││
││ └─┘ └┘││ │ │└┐│ └─┘└┘ └┘││└┘ │┌┘ ││ │┌┘││ └┘ ││ └┘ └┘││└┘ ││└┘ ││││
└┴──────────┴┴──┴─┴─┴┴───────────┴┴────┴┴───┴┴─────────┴┴─┴┴─────────┴┴─────────┴┴────────────┴┴───┴┴┴┘
In[5]:](/photographs/automatic/2026/10/14/adding-plots-to-nota.webp)
![Input Nota Code:
- fibonacci sequence at[n] = ((1 + Sqrt[5]) ^ n - (1 - Sqrt[5]) ^ n) / (2 ^ n * Sqrt[5])
- first digit[x] = get[integers[x], 1, 1]
- plot[[first digit[fibonacci sequence at[x]] | x <- iota[100] ], 10]
And renders:
n n
╭ ___ ╮ ╭ ___ ╮
│ 1 + ╲╱ 5 │ - │ 1 - ╲╱ 5 │
╰ ╯ ╰ ╯
In[1]: Fibonacci Sequence At[n] = ─────────────────────────────────
n ___
2 × ╲╱ 5
Out[1]: 0
In[2]: First Digit[x] = integers[x]
1,1
Out[2]: 0
╭ ⎡ ⎢ ⎤ ╮
In[3]: plot│ ⎢ First Digit[Fibonacci Sequence At[x]] ⎢ x ∈ Ɩ[100] ⎥, 10 │
╰ ⎣ ⎢ ⎦ ╯
╭─────────────────────────────────────────────────────────────────────────────────────────────────────╮
│ ╭╮ ╭╮ ╭╮ ╭╮ │
│ ╭╮ ╭╮ ││ ╭╮ ││ ╭╮ ││ ╭╮ ╭╮ ││ ╭╮ │
│ ││ ││ ││ ╭╮ ││ ││ ╭╮ ╭╮ ││ ││ ╭╮ ││ ││ ││ ╭╮ ││ │
│ ││ ││ ╭╯│ ╭╮ ││ ││ ││ ╭╮ ││ ││ ││ ││ ╭╮ ││ ││ ││ ╭╯│ ╭╮ ││ ││ │
│ ╭╯│ ╭╯│ │ │ ││ ││ ╭╯│ ╭╯│ ││ ││ ││ ╭╯│ ╭╯│ ││ ││ ││ ╭╯│ │ │ ││ ││ ╭╯│ │
Out[3]: │ │ │ │ │ │ │ ││ ││ │ │ │ │ ││ ││ ││ │ │ │ │ ││ ││ ││ │ │ │ │ ││ ││ │ │ │
│ │ │ │ │ │ │ ╭╯│ ╭╯│ │ │ │ │ ││ ╭╯│ ╭╯│ │ │ │ │ ╭╯│ ╭╯│ ╭╯│ │ │ │ │ ╭╯│ ╭╯│ │ │ │
│ ╭╯ │ ╭╯ │ ╭╯ │ │ │ │ │ ╭╯ │ ╭╯ │ ╭╯│ │ │ │ │ ╭╯ │ ╭╯ │ │ │ │ │ ╭╯ │ ╭╯ │ ╭╯ │ │ │ │ │ ╭╯ │ ╭╮│
│ ╭╯ │╭╯ │╭╯ │╭╯ │ ╭╯ │ │ │╭╯ │╭╯ │ ╭╯ │ ╭╯ │╭╯ │╭╯ │╭╯ │ ╭╯ │ │ │╭╯ │╭╯ │╭╯ │ ╭╯ │ │ │╭╯││
│╭─╯ ╰╯ ╰╯ ╰╯ ╰─╯ ╰─╯ ╰╯ ╰╯ ╰─╯ ╰─╯ ╰╯ ╰╯ ╰╯ ╰─╯ ╰─╯ ╰╯ ╰╯ ╰╯ ╰─╯ ╰─╯ ╰╯ ││
╰┴───────────────────────────────────────────────────────────────────────────────────────────────────┴╯](/photographs/automatic/2026/10/14/pattern-of-fibonacci-s-first-digits-with-nota-nota.webp)
