Alchemy

Generate any a-by-( b + c ) finite rectangle SVG containing potentially Infinitely many a-by-( 2 * b ) finite rectangles animated along a number line of ( ( c - b ) / a )^n scale symmetry.

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/learn @bestape/Alchemy

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README

for MozFest, 2021

During the workshop, we'll have fun with:

https://bestape.github.io/alchemy/

We'll discuss (c - b)/a as well as a*(x^0) = 2*b*(x^1) + a*(x^2).

<details> <summary>Before the workshop, please visit:</summary>

</details> <details> <summary>A question to ponder, "Is the Harmonic Series convergent or divergent, given the correct 'resonant' base?":</summary>

</details> <details> <summary>If we have time, we might explore how integer sequences as music relate to `a*(x^0) = (x^(y – 1))*(a*x + 2*b)`:</summary>

For instance, https://www.instagram.com/p/B6MDtg9AJqH/

</details> <details> <summary>Additional resources:</summary>

PBS SpaceTime about Vera's Metallic Means: https://youtu.be/MIxvZ6jwTuA
Mathologer about visual Infinite descent: https://youtu.be/ubHVK71F01M
Numberphile about Golden ratio irrationality: https://youtu.be/sj8Sg8qnjOg

</details>

Above: a from iteration, to recursion photograph-stack stereogram use case.

alchemy

an animated SVG printer using a PythagoreanMetal engine

!!! TIP JAR !!!

!!! MERCH !!!

Above: a stopwatch that uses 75% of the remaining parent area to count in loops of 60 seconds, 60 minutes and 24 hours.

!!! TIP JAR !!!

0. contents

<details> <summary>contents</summary>

what
use
options
example tiles
technology
why
problem & opportunity
how
next
app.js
paths
to do
license

</details>

1. what

Create vanishing point cellular automata moving images like the famous Golden Ratio:

These images can be used, among other things, as a box of Infinite objects with every object observable from above.

Make Infinite copies of yourself. Super selfies!

selfie

!!! TIP JAR !!!

2. use

<details> <summary>details</summary>

Have node.js installed on your machine;
download the app.js and app.json files; ensure app.js is executable;
change the values in app.json to your preference;
run ./app.js in your terminal; and
enjoy the SVG printout!

</details>

3. options

<details> <summary>options</summary>

Please read app.js.

The app.json file lists the options.

Change its values to the choices you want then run app.js in a terminal with Node.js installed.

| option | type | description | | ---------------- | ------- | ---------------------------------------- | | a | number | repeating rectangle's horizontal measure | | author | string | the person who made the program | | b2 | number | repeating rectangle's vertical measure | | background | string | parent rectangle's colour; can be null | | borderColour | string | parent rectangle's border colour | | borderSize | number | parent rectangle's border size >= 0 | | cellBorderColour | string | repeating rectangle's border colour | | cellBorderSize | number | repeating rectangle's border size >= 0 | | clickStart | boolean | false = auto; true = manual | | colours | array | repeats if too short; [0] only for start | | cork | string | remainder rectangle included if colour | | drawPath1 | boolean | path shown if true | | drawPath2 | boolean | path shown if true | | drawPath3 | boolean | path shown if true | | drawPath4 | boolean | path shown if true | | embed | boolean | use to copy/paste code into an SVG file | | file | string | file name and relative path | | id | string | combine with other code; use with embed | | images | array | repeats if too short; [0] only for start | | lead | boolean | false = a repeat begins from the top | | loop | boolean | animation auto restarts when finished | | offset | object | use with embed and id to add to SVG file | | opacity | number | between 1 (opaque) and 0 (transparent) | | pause | string | delay until next animation starts | | png | boolean | false = jpg | | repeat | number | number of repeating rectangles >= 1 | | speed | string | the time it takes to move by 1 exponent | | vertical | boolean | repeating rectangle starts vertical | | viewBoxAdd | object | the width and height axis canvas size |

If you need to calculate a number option:

open and edit app.js;
mute the option in the App(){ ... } constructor function with //; and
write the modified option below the muted option.

Please see the this.a option in App(){ ... } for an example.

</details>

4. example tiles

<details> <summary>example tiles</summary>

To run the following animations:

click on the image, it'll open in a new tab; and
within the new tab, click on the repeating rectangle at the top of the parent rectangle.

Vera's Metallic Means can be SVG printed by app.js:

set the a value in app.json to 100; and
set the b2 value in app.json to 100, then 200, then 300 and so on.

As a continuum rather than a natural count, the Metallic Means are SVG printed by app.js whenever a <= b2 ( a is less than or equal to b2 ) in app.json.

Here's the first Metallic Mean natural count, the Golden Ratio:

Here's the fifth Metallic Mean natural count:

As b2 tends toward Infinity, the repeating rectangles quickly become invisible to the naked eye.

Here's the tenth Metallic Mean natural count, with a = 100; b2 = 1000 in app.json:

However, if b2 <= a ( b2 is less than or equal to a ) in app.json, the repeating rectangle takes much longer to become invisible to the naked eye, and not because of x scale exponentiation.

Here's the second natural count in the b2 <= a direction:

Here's b2 <= a when x = 99 / 100, in other words no irrational parts but still non-halting, using this formula:

As b2 approaches a magnitude Infinitely larger than a, the automation approaches a more accurate non-halting definition of 2^( 1 / 2 ). Compare the anthyphairesis of 2^( 1 / 2 ).

A natural PythagoreanMetal order measures ax with b2 unity or b2x with a unity.

ax = b2 is ISO 216, using this WolframAlpha calculation:

2ax = b2:

ax/2 = b2:

ax/3 = b2:

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