Lepidopterally yours

Despite what you may think, I don’t just spend my time sitting at the computer composing posts that apparently get less and less relevant with every passing day. I still go walking, both alone and with companions, both here on the Kaiserstuhl and in the Schwarzwald. Yesterday (Saturday) was an example. I’d promised myself I’d do that milk run of mine – the 14 km back from Endingen – and despite the weather not looking too promising I started out.

The first hour out of Endingen is an uphill traipse made amusing only by the story of the road signs (‘The quick change act’, posted in June 2017). Yesterday it was warm and still and decidedly humid, and I was glad therefore to get up out of the woods and onto the crestline path. It was time then also for a five-minute break. From then on things went brilliantly, especially as the sun came out and the breeze freshened. My route for the next hour took me along the edge of the dry grasslands – the Trockenrasen – that characterise the centre of the Kaiserstuhl. There, flying everywhere, were hundreds of butterflies, particularly of a species that I’ve subsequently discovered is called the Weisser Waldportier (https://www.deutschlands-natur.de/tierarten/tagfalter/weisser-waldportier/); in English it is called the Great Banded Grayling (https://en.wikipedia.org/wiki/Brintesia). There were dozens of these wonderful things – they’re large and very distinct – and they were flitting around everywhere I looked. They were far too fast for me to photograph, so you’ll have to believe this picture from the internet (http://www.lepiforum.de/lepiwiki.pl?Brintesia_Circe).

Brintesia circe

Evidently they love this type of environment and evidently they fly from June to September. Yesterday was ideal, and I had the privilege of being there to watch them.

Lepidopterally yours etc.

Yet more interweaving…

I can readily understand it when people suggest my thought processes are not straightforward. That’s obvious whenever you read this blog. Yes, walking is of course the blog’s principal theme, but it’s far from being the only theme. And when you look back on the past five years of posts – 356 at the last count – you find that all the themes are interwoven. Thus walking is interwoven with geology which is interwoven with fashion which is interwoven with commentary which is interwoven with humour which is interwoven with music which is interwoven with philosophy which is interwoven with religion which is interwoven with language and so on. Clearly I like interweaving. Let’s do some more!

The ripple field

The dress

You’ve seen one of these pictures before – the one showing the field of sand ripples in Death Valley. I used it a few posts ago (‘Firmly back on track’) as an example of a readily discernible spatial pattern. The other picture (which shows a ribbed cotton maxi-dress available from a Manchester-based online fashion retailer catering to the teenage wallet) is – believe it or not – another example of that very same pattern. In each of the examples there is a set of more or less parallel ridges which in places bifurcate. The difference between the examples is only in the degree of parallelism of the ridges and the regularity of the bifurcation.

Now suppose you have to construct those two examples. In the one case you have a stock of meticulously prepared cotton yarn and a factory full of expensive machinery; in the other you have some grains of sand and the wind. The construction process in each case will be a spatial process (obviously, because the pattern being constructed is a spatial pattern), but the two processes will be radically different in their nature. The process involved in constructing the dress material will be completely predictable – the machinery will do exactly what you tell it to do when you start it up. In contrast, the process involved in constructing the ripple field will be largely unpredictable. What will happen at any particular point at any particular moment will depend on the availability there of moveable sand grains and on the instantaneous wind strength and direction. The first process is capable of producing sets of exactly parallel ridges with regular bifurcations exactly where they’re wanted; the second can never produce other than a set of approximately parallel ridges with irregular bifurcations.

Some of you will see where I’m going with this. It’s the distinction between processes that are deterministic and processes that are stochastic. A deterministic process – for instance the process involved in constructing the dress material – is one that always produces the same output from a given starting condition or initial state. A stochastic process – for instance the process involved in constructing the ripple field – does not always produce the same output for a given input; there is chance involved. That’s where things start to get really interesting. Watch this space!

This is for anyone from Missouri

The titles of the posts in this blog are not always full of promise; the posts themselves are nonetheless often full of promises. Thus three posts ago (‘Firmly back on track’) I promised you (1) a computer program that would let you randomise images, and (2) a test you were bound to fail. You had that test in the subsequent post (‘Spatialness for Fashionistas 101’) and you had the solutions for it in the post after that (‘The test solutions, the take-home message, and some great music’). So where’s that promised program? Don’t fret! It’s here. theendtoendblog keeps its promises!

You’ll find full documentation of the program – CODING – in ‘Software’, one of the pages at the left-hand side of the blog. There are details there of how to get the program and of how to use it.

Which leads back automatically to the title of this present post, for you’re surely asking yourself what on earth an image randomising program could have to do with Missouri. Hint: check out the meaning of the phrase “I’m from Missouri”. Got it? Yes, it means simply “Show me!” You’ve had those images of the fabrics and you’ve seen the spatial patterns from which they were obtained. Now you need to be able to prove for yourself that you can go from one to the other and back again. Spatialness out; spatialness in. This is what the program does. Moreover, it will do it for any image you give it. (There are a few restrictions but not many: these are given in the program documentation.)

No, I won’t describe the algorithm the program uses, nor will I give you the program’s source code.

Have fun!

 

The test solutions, the take-home message, and some great music

That test wasn’t too difficult, was it? Here are the solutions. For each fabric there is, from left to right, (1) the image you were given, (2) the spatial pattern, and (3) the source picture. I’ve indicated the designer of the fabric and the date, insofar as I can identify these.

First the three ‘stripes’…

A: Moschino Fall 2020 Ready-to-Wear

F: Elisabetta Franchi Fall 2020 Ready-to-Wear

J: Saint Laurent Spring 2014 Ready-to-Wear

…then the three ‘patches’…

B: Versace Fall 2018 Ready-to-Wear

E: Balmain 2012

L: Zimmermann Fall 2019 Ready-to-Wear

…then the three ‘meshes’…

G: Unknown designer 2010

I: Unknown designer 2018

K: Mulberry 2016

…and finally the three ‘grids’…

C: A.L.C. 2015

D: Emanuel Ungaro Fall 2013 Ready-to-Wear

H: Atelier Versace Spring 2015 Haute Couture

How did you do? Not very well? Oh, sorry, but I forgot to tell you that in every case I’d randomised the image of the original spatial pattern. The images you were given were therefore ones in which there was absolutely no spatialness. It’s not surprising you couldn’t identify the patterns correctly.

N.B. Some of you undoubtedly thought that this was a multiple-choice test and therefore that you could pass (or at least get close to passing) by choosing your answers at random. No such luck! Yes, it was indeed a multiple-choice test, but it was one in which you were told in advance the actual number of patterns of each type. Let’s set the pass mark at better than 50%, i.e., more than 6 correct out of 12. The chance of you passing by choosing your answers at random is then less than 1 in 50; the chance of you doing reasonably well (more than 9 correct out of 12) is less than 1 in 10000. If you say you recognised all the patterns correctly, then either (a) you are the next Karl Lagerfeld, or (b) you are phenomenally lucky, or (c) you are telling porkies.

The take-home message is a very simple one: you can’t study spatial patterns correctly – no matter what they are – if you ignore their inherent spatialness. You can no more take the spatialness out of a spatial pattern than you can take the honky tonk out of the girl. Which of course leads some of you to reach out for your old Brooks & Dunn cds. Or at the very least to load the appropriate video: https://www.youtube.com/watch?v=Si0azctmJDc.

I promised you some great music!

‘Spatialness for Fashionistas 101’

Those of you who’ve been conscientiously enrolling in ‘Introductory Geology’ will be fully aware of the necessity of selecting suitable subsidiary courses. I’ve taken the liberty of pre-enrolling you now in one that really is a must – ‘Spatialness for Fashionistas 101’. I hope you don’t mind.

I say ‘pre-enrolling’ because there’s a small catch: you’ve first got to take a short aptitude test. Don’t worry, it’s a straightforward multiple-choice test. You’re given a set of twelve pictures and you have to identify the patterns in the fabrics that are shown there. There are four possible types of pattern: stripes, patches, meshes and grids. In the twelve pictures there are three examples of each pattern type. The pictures are all either runway shots or photo-ops, therefore they are of fabrics that are being worn. Don’t expect then that the patterns will be absolutely regular or that they will be absolutely standard. To get you started, here are some examples to show how they might appear.

And now here are the pictures:

A

B

C

D

E

F

G

H

I

J

K

L

OK, that doesn’t look too difficult, does it? Remember that there are three examples of each of the four pattern types. Write the pattern type against the picture’s index letter. Hand in your paper as you leave the exam room. I’ll have the results for you in the next post.

Best of luck!