helluva lotta html tabs (or an excursion into geometry and number theory [or a mandala of a jungian archetype])

webpage of nested tabs header

I’m afraid of making a webpage of nested tabs (the tabs would be something like jqueryui.tabs).

jqueryui tabs homepage snapshot

It would truly have a lot of tabs, as I imagine it.  Each tab would have as many tabs as every tab in its layer (see below, but this is actually probably false, but is a good heuristic).  I would label each tab header with its count, too.  I’m afraid to even calculate how many there would be.  It would be a function of the size of the browser window and the size of the tab headers and the tab implementations css margins and paddings, etc.  However, it would be further complicated by the fact that width of a tab-header is going to change because the tabs are going to be labeled by the tabs position in the actual linear process of creating the tabs.  Thus, as more tabs are added and the string representation of the count of the tab in the overall linear process of creating the tabs increases so too will the width of the tab header and thus will decrease the number of tabs that can fit in a particular tab page.  Luckily, the height of the tabs can be assumed to be constant.  Ooohhhh, no it can’t.  As the tab page <div> width and height decreases due to the layered nesting of the tabs, there is going to be less measure available for the vertical or horizontal tab header, until, when the linear count string representation is large enough, the tab header text will wrap and thus double (triple? quadruple? …?) the height of the tab header.  One could probably find their way to an upper bound for the depth of ‘triple’ and ‘quadruple’ etc (on second thought, you couldn’t, probably, because depending on the seed algorithm, later layers may have far more than earlier layers and thus this is fraught with difficulty, too).  As I imagine this all working, tab pages would cease nesting (in a particular branch) once there was no more room in the parent tab page for another entire header containing the position text.  Furthermore, each layer, as shown in the crude drawing, would alternate loop around vertical and horizontal tab header directions going clockwise.

At least, that’s how I imagine this, assuming a browser could even get anywhere near a full representation.  I’m sure a single ‘layer’ could be fully displayed using an algorithm that nested inwards always on the layerth tab position of next nested layer (but it would still have boatloads of empty tabs to create [or you could loop in always from the outside most layer until that horizontal or vertical linear collection of tab headers would wrap to a second line if another were added).  In that way, the thing would be sort of spirally flat.  But this would also change how many tabs could possibly be created due to the fact that the flattened spirally first layer will have tab header text that has all low-count numbers.  Almost assuredly less than 50000.  I mean, I’m looking at my 1920×1080 monitor (lets assume full screen) and referencing the jqueryui.tabs visual above to guess the flattened first layers number of tabs using the labeling scheme mentioned.  What is that, like 50px tall and, starting at 1 and counting to 50000, going to maybe 100px wide.  It would vary as the count grew, and even with each number, subtly, in any particular non-fixed width font.  With this particular seed algorithm, we’re basically talking about fitting a number of slowly growing squares onto the screen, where each square contains a number increasing by one for each new square on screen.

That algorithm is boring.  It’s just limited to flatness because of concerns for overloading the browser rendering engine or even for exceeding the upper bounds of the underlying numerical type in javascript.

It would be interesting to develop an equation that could exactly calculate the total number of tabs and the number of tabs on a particular browser window environment.  You could create fancier calculations, like how many tabs are visible on a particular tab page given the position of that tab page in the linear count of all tab pages.  But even that ignores the most interesting aspects of the webpage of nested tabs, such as how each of all the hidden tabs reveal a collection of tab headers containing numbers which are initially determined by the seed algorithm.  And that’s the rub, any difference in the seed algorithm is going to totally change any calculation concerning how many tabs there are total and what tabs are visible on any particular tab page.  Furthermore, any particular focused tab will begin to show different content than that initially determined by the algorithm as the user clicks through the nested tabs and moves up and down layers of the webpage.  (Think of how on each page filled with tab page headers, you can click one and see a new nested tab page filled with tab headers containing numbers, and then click again, and again, and mix them up, and then go backwards and forwards.  Now try to predict which tab headers will be visible when a particular tab header is clicked.  It would be difficult even without the mixing up of the tabs.  But how could that history be represented and serialized (programmer talk for written to some sort of data format to be stored in memory) as it occurred in such a way as to facilitate an easy calculation of what is visible on any tab page?  Alternately, what could such a calculation and such a representation be similiar to?  Could arbitrary, non browser environments, or “zooming” geometries that don’t restrict nesting at all, be meaningful?

Scary stuff.  Here’s its genesis:

webpage of nested tabs

(I’ll change this photo as soon as I have access to my normal camera)

Of course, hidden in all those details of a particular implementation of the idea in an html browser using javascript is something a little more general concerning numbers and geometry (each layer could correspond to a prime number, for instance, and all the nested tabs would be composites of that prime number, with each of those revealed nested layers being prime numbers as well and powers of composites for the container’s prime factorizations).   I wonder if there is a correlate physical/energic process/structure?  (totally way out in left field, there [coming back around, I love how I injected that comment since this whole entire post is way out in left field!]) I wonder if you could create connections, or tunnels between tab pages, so as to count through them all efficiently and to learn paths and maybe even ways of walking paths if there could be some sort of meaningful geometry that could be moved through…

And behind this entire gestalt is probably an active archetype, a la Jung.  I especially appreciate the lightning crease that tears down the middle of the page.  I had printed a document earlier and I remember when the printer made a sharp sound and the creased page had been ejected.  But at that time I didn’t know this iridescent archetype was going to paint itself over the top (of my night, too, ultimately, since overall I’ve devoted from 3 to 5 hours to this flowering mandala from outhe blue).

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