The ultimate Help section
to detect Golden Spiral in your images

After so much effort, the final realization could not be missing, the one for which each of us can put into practice how much it is possible for him to de­vel­op au­then­tic golden spirals, applying them or better, obtaining them from living cre­atures, instead of so many superficial mystifications.
To this end, I have taken the first model tested on the mytilus edulis and dem­on­strat­ed there with a first composition tool, to build a complete and versatile one, although still rudimentary, functional enough to allow a direct online ap­proach.
It integrates the console already proposed – but which would remain an ab­stract experience – with the addition of some commands necessary both for load­ing and positioning images on them, and for manipulating and adapting the spirals on them, until discovering the most suitable one for individual cases.
It was started for my personal use, in order to be able to verify and dem­on­strate those geometric principles that I had focused and deepened at pi-day.­eye­-of­-rev­e­la­tion­.org; but after several functional implementations it has be­come a tool from which everyone can take advantage and knowledge.
It is important to bear in mind that it is a console developed directly in HTML5 for a single web page, therefore kept essential in terms of layout and usable space. Therefore it will be necessary to pay some attention to a sequential and correct use of the same, since some parametric fields serve more than one function and will have to be updated passing from one to another; otherwise, unexpected and inconvenient results may occur (even for the writer); but the greatest risk is having to refresh the spirals, or the page.

To deal with it immediately, the already existing keyboard has been added – although ultimately – the button , skew, used to incline the spirals horizontally and/or vertically; a command that should be used last and /or for slight adjustments to any three­-di­men­sion­al pho­to­graph­ic perspectives, as explained later.
It is the most delicate and unpredictable to use, difficult but in some cases very useful, for those who have patience. Its execution draws on the pa­ram­e­ters en­tered in the x and y fields and in order not to leave too much sur­prise, it will appear bordered by a turquoise dotted line.

The horizontal and vertical ruler with 5px clicks arranged at the top of the screen can ul­ti­mate­ly be moved with the mouse to any point on the whi­te­bo­ard to measure distances quickly.
Because its effective image even if transparent is superimposed, its internal area once activated will prevent access to commands internal to its pe­rim­e­ter, depending on the position.
On the other hand, it can then be dragged to any point of the screen by sim­ply keep­ing the mouse clicked on any point in this area.
However, the cursor will be able to leave it to click commands that are ex­ter­nal to it and, for greater convenience, touching it again will au­to­mat­i­cal­ly bring it back to the corner position of the screen.

Now the image: get+ invites you to choose a file from your system or by en­ter­ing a URL. It will be placed at x:15px, y:430px of the board in its native size.
The browser may or may not supply its width in the width field, from which the size may be varied proportionally, and shifted according to the number of pixels entered in x and y; can also be rotated, by . degrees, by sim­ply clicking the numeric field, while the button to the left can now act in­de­pend­ent­ly to flip and display (lit up color) the direction of rotation of the spiral, which can be multiplied and superimposed in both ways.
All this with the put button, while - will mirror it horizontally combined with the other parameters, in order to keep the current positioning.
For a vertical reflection just combine it with a 180° rotation [put: x=0, y=0].
To cancel horizontal inversion, click the same button.
Combining various options had the aim of keeping the layout of the com­mands as compact as possible, in a dashboard suitable to perform composite op­er­a­tions in a practical and intuitive way, but in a single HTML5 screen; and it is evolving according to the needs that emerge by experiencing them; be­cause programming never ends (so, please, be patient if something won't run as ex­pect­ed – a clear feedback may help).
It's all contained in three horizontal panels, the first to draw spirals, the second to manage them, the third essentially oriented to images.
Regarding the image to be loaded, a piece of advice for the more expert would be to modify its format before uploading it, so that what would be its ideal cen­ter for the spiral is at the vertical and horizontal center of the whole picture; an example is on the side; it is not always easy to identify it on the photos, but it can make much more practicable and fruitful the options, which will act around that center and not at the random center of the image. Even if the spiral itself can rotate, this could optimize the placement of images of a certain size, since the x, y coordinates do not accept negative out-of-frame values.
Here is an image tak­en from the web, re­sized with the dark back­ground to the right and be­low, show­ing its own cen­ter in white, and by the gold­en ar­rows ex­tend­ed in red the prob­a­ble cen­ter of the spi­ral, which in this pan­el is just the one at 144°, and it would be enough to rotate the shell 20 or 30 degrees on the support to see it coincide.
Further attempts at trac­ing, how­ev­er, dem­on­strate what may be o­ver­looked at first sight, name­ly that the shot, aimed at en­hanc­ing the beau­ty of the ob­ject, en­hances its ex­ter­nal part with a shot that is not fron­tal e­nough (should I say or­thog­o­nal?), which height­ens the pro­por­tions of the ex­ter­nal volute by re­duc­ing the in­ter­nal ones in per­spec­tive.
To be able to declaim instructive results, it is finally worth taking note of eve­ry­thing that can lead to misrepresentation. In any case you have to deal with the focal length of the photographic lens and the depth of the body.

In summary x, y, width and rotation will be managed together by the second row buttons, while x and y will also apply to the tilt button, so you need to up­date the contents in the rare case of switching from one to the other.
This choice bascally made it possible to keep the commands clearly visible on a contained operating space.
One or more new ver­sions, not im­prob­a­ble, could op­ti­mize eve­ry­thing; but it should be con­sid­ered that this con­sole was born and raised in a few days with on­go­ing re­search (ex­am­ple at the side), and is not in­tend­ed to re­place heav­i­er and more com­plex ap­pli­ca­tions, which re­quire spe­cif­ic in­stal­la­tion and ex­per­tise, but ra­ther to of­fer those who want it a di­rect and han­dy ac­cess, to con­front the true gold­en spi­ral in all its forms, re­plac­ing mean­ing­less graph­ic ex­pe­di­ents with a well-founded ex­per­i­men­tal path.
A print to file via a PDF print­er (which can be in­stalled vir­tu­al­ly, even with­out owning it, and ren­ders ja­vas­cript spi­rals bet­ter than a PDF print from a brows­er) will be able to save the ob­tained re­sults quite well.

Finally, some useful accessories to intervene with effects on the visibility and contrast of details, enabling or inverting the background colors, to better adapt the screen to each type of image in use.
First, three quick options: paper, white and clean, the latter uniforms the back­ground to the homogeneous paper color, thus reducing the possible problem of sep­a­rat­ing the paper background in a screenshot to be processed in a graphic ed­i­tor for some photo montage which, at least for now, seems to be the most practiced resource.
They won't be accessible anymore after using the following system ones.
The colored or white button to the left of opens an HTML window for choosing a page background color; the field to its right allows the practical one to enter a predefined #HEX, in the format #FFF or #FFFFFF which, if valid, will take precedence. Clicking in fact will activate one or the other.
There are also as [on/off] switches:
  to reverse image and dashboard (e.g. with: HEX #0080C0), and
  to highlight the golden outline, if needed on an image.

graphic rotation of the spiral
In the early stages of this study, whatever the length of the ray, the spiral al­ways started from the zero angle of the JavaScript, 270° in the PostScript notation I used in the images and blackboard background, 6 o'clock on the clock.
spiral rotation · 10°, 50°, 100° · radius rotation
Changing the radius rotates the spiral with respect to any previous try, in some cases disorienting the operator; since the modification intervenes on the entire placement of the spiral on a background figure, it can bring the solution closer to or further away, having to rearrange the ratio and rotation parameters which for a spiral is equivalent to a zoom.
In fact, it is important to bear in mind that while the spiral can be rotated with re­spect to the centre, this can simulate an only apparent zoom effect with re­spect to the loaded image, since the effective inclination and extension may not cor­re­spond diametrically to those of the figure, leaving only a frustrating sense of im­pos­si­bil­i­ty. Changing the starting radius in this mode can solve the prob­lem; or alternatively you can rotate the image, but it is a maneuver that becomes prob­lem­at­ic when it is repetitive, if the above advice has not been applied.
To clarify the matter, I have therefore inserted a new mode, in addition to the first, which allows you to trace each spiral in a single way, keeping its o­ri­en­ta­tion un­changed for any radius, which will rotate by placing itself in the angle of the curve that belongs to it.
They can satisfy different needs; in this way however, once the rotation of the spi­ral has been established with respect to an image, its starting angle can be var­ied with­out having to readapt it.
The button * represents the state of the second (default), which alternates in * for the first one, and vice versa.

april 2023
In addition to a visual improvement to the dashboard, the last two buttons added: –– and ––, allow you to store the 10 numeric parameters in use, to be able to recall them after having tested and discarded others on the same page, until it is re­loaded. So the second, with blank memory, can serve to clean up all the parameters, when they are no longer useful.
The golden spirals
With research matured in contrast with the most widespread conceptual and pragmatic improvisation, which is worth little more than zero, in the effort to propose order, it is now clear that the same first conformations of the golden spiral examined in this page, based on the 4 concentric circles in the ratio φ from which it started, are by no means sufficient to embrace all the phe­nom­e­no­log­i­cal categories of cases.
The golden expansion already demonstrates in nature that it has no bound­a­ries, and I should only add buttons.
The function 8 comes to meet us precisely to make up for this deficiency and discover new proportions, it being understood that each case is on average attributable to certain golden proportions – the only ratio that has own mean­ing – attributable to a category that classifies it currently, rather than referring it to isolated logarithmic spirals that define nothing at all.
Superimposing spiral designs on galaxies is all too easy and free; suggestive and educational at first, but then devoid of cognitive progress.

may 2023
visual Diaphragms and Perspective
By experimenting with the first and most common prototypes of spiral or­gan­isms in this elementary research, with hints and solutions at the Gallery of the operating console, above all in trying to apply processes of multiple spi­rals to vegetables, which are the most evident bearers, I had to take note of a problem that accompanies more or less all photographic shots, even the most accurate ones, deriving from the practical impossibility of guaranteeing a centered and orthogonal shot to three-dimensional round shapes, and con­se­quent­ly to identify the virtual center in 2d.
Add to this the diversity between coils which, although growing si­mul­ta­ne­ous­ly on the same plant, develop with their own volumes and den­sities, nat­u­ral­ly e­lud­ing any geometric scheme governed by a single formula.
For both reasons, it is difficult to establish the true center of motion, or where the spiral actually begins.
To resolve any doubts as much as possible, I have reproduced spirals in ro­ta­tion in the round several times, creating an internal geometric area which, based on a starting radius centered on the most regular area, helps to verify if the chosen center corresponds more to that sample.

The idea arose on this first multiplication test (old dashboard and code), in an attempt to see the spirals that regulate the external crown of the in­flo­res­cence collimate, which gave me a more precise perception of the center than the overall view . A different accumulation of tubulosis in circle can in fact easily give an optical illusion.

To facilitate this kind of control, I have inserted an option that draws with a single click the number of desired spirals, dividing the 360° by the desired number and automatically updating the rotation value of each one.
To do this, just add the minus sign (-) to the value of the new s-pinwheel field (a pinwheel of spirals) and then click once the selected spiral's button.
Of course, repeating it will increase the thickness of the curves; and also gen­er­ate particular graphic effects by repeating with an approximate rotation angle.

Beginning from the start radius of the spiral, which a negative value makes invisible, I wanted to add other options that offer curious implications, making visible or not the line-segment that connects each sub­se­quent spiral arc.
Together with the sign ± for the visibility of the ra­di­us, one or the other effect can be obtained with its value being respectively odd or even, a difference that does not alter a test of a certain size; whereas the length of the spiral reserves unexpected but stimulating schemes. Applied to samples of the gallery, of previous en­cod­ing, it develops very particular effects; but i think i will fix it.
seleziona uno ad uno i modelli a lato

I will show just a few ex­am­ples. The various combinations, which the console allows you to test, can pro­vide sug­ges­tions for new ways of deepening.

However, having reached a first level of experimentation and centering of the multiple spirals, the intrinsic factor of the camera angle remained, which had to be compensated, albeit relatively, by a function that could correct the per­spec­tive view of the spirals, unforming them as far as possible to that of the object in the photo.

Perspective correction is equivalent to viewing the 3D object from an observation point at a variable distance.
In particular, the closer the distance is, or the photographic lens is wide angle, the greater the perspective effect.
In my console it can take place in two ways: frontal pivoting on the x axis, or more rarely lateral pivoting on the y axis.
In both cases it is possible to interact with two parameters: the value of rotation (suggested between 1° and 80°) and the distance , not needed, as it defaults to 4,000px (say, between 1,000px and 10,000px).
The procedure will select the two values from the fields zx and zy (added on pur­pose), starting from the value zy for ease of exclusion, distinguishing their purpose according to to the entered value.
Therefore, if for example: zy = 30, zx will not be considered except for the possible distance, having a much great­er value.
Normally it will be enough to vary the field zx, since the perspective alterations are more likely consequent to a frontal shot, more critical vertically than lat­er­ally.
The perspective is operated with the ' button, which remains active and un­changed according to the start-up parameters, as long as it is kept on.
To use modified parameters it is therefore necessary to switch the button off and on again.
It is independent of the spirals, which it conditions before or after they are traced; and obviously does not alter the uploaded images.
(This may not work under Windows XP (unless you maintain a 100% zoom of the page), so to use the other options under this operating environment, you will need to be sure to set it to zero).
A turquoise dot border highlights its effective perimeter shape, which de­ac­ti­vates by turning it off. Here is an example of the zx graphical view, obtained with the new version of the dashboard:

the entire trapezoid
outsides the
visible window
As you can see in the image, I had to make the command keyboard more com­pact, to add the data of the new function.
I therefore focused on zx and zy both the introduction of the perspective pa­ram­e­ters, and those of skew, less likely to be used, without leaving them su­per­im­pose on those of the image positioning, always necessary in parallel.
Since – – retrieve the setting stored by – – superimposing it on the current one, I added the command – – i.e. exchange of the current par­a­met­ric plan with the stored one.
This way you can continue to test and compare both without loss.
Command-switches not accompanied by numerical values may not be mem­o­rized, since their arrangement depends on various factors in the script; they will need to be manually reconfirmed where appropriate.

I noticed that keeping the parameters introduced in the page even by refreshing it (Ctrl-R) depends on the browser; however this procedure is tested only on an outdated Firefox and on some chromium engines; also because each update is a growing danger.
It should be clear; I tried to keep the functions interactive but independent, for maximum operational flexibility; a little getting used to will make everything com­fort­a­ble enough.
Anyone who has followed me up to here will understand the effort and the con­ve­ni­ence of some compromises, in the descriptions and illustrations at al­ter­nat­ing stages, given that all the work has grown in the course of the research and its publication, while the limits of space (and of time) have remained the same.
Basically it is a single web page of less than 40k, Gallery and Info included, plus 12k of javascript and a style sheet.

I therefore hope that this tool I have created can help unravel this fascinating hank.

continues… thank you for sharing;
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if you want to post some good result, send it with the whole dashboard to the @ If at least three people, I 'll put the figures in a gallery, with names and links