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Useful Links

One of the things we did when we first built websites in the late 1990’s was to provide lists of links which might be useful to other people. Better search engines and dominant marketplaces have limited the use of a “List of Links”. Undeterred by fashion, here are the various links to areas I’ve found useful in recent months, particularly regarding the geoscience consulting business. Practically all consultants have a website and actively use connections within LinkedIn, however, in geoscience there is not a single place to go for clients to find commercially available products and consulting services. Or if there is please let me know about it.

Please feel free to add your own favourite links in the comments and I will add them to the list.

WebsiteG&G project based and Consulting Services
xcovermatch talent to hosted projects and provides hosted virtual workstations (backed by Shell). Not too many projects presently, but one to watch maybe.
proteusprobably not a major player in G&G to date, but could be a future option if more projects are added and it gains traction beyond the engineering sphere.
syntillicaproblem solving and consulting services across the energy industry
nudgeexchangefreelancer marketplace for energy industry
WebsiteTraining Course Websites
book-4Listings of various training courses available, both free and paid.
tonntaMay as well link myself ! We provide a shopfront for consultants to sell services such as consulting time, documents, codes, training courses and manuals.
WebsiteGenerally Useful Marketplace Listings
seg marketplacecomprehensive listing of geophysical companies and suppliers, but could use a website refresh.
petromehrasHas comprehensive listings of all types of software used in the energy industry
WebsiteConsultants Marketplaces and Job Listings (also with links)
A variety pf marketplace websites can be used to find consultants in the IT sector at rock bottom prices, but these are rarely used in geoscience. The concept is good but some of the projects offered might be considered questionable at best. Typical examples include freelancer upwork truelancer toptal peopleperhour
fiverrA few G&G services on offer from freelancers on this website
job listingsA variety of websites such as indeed simplyhired glassdoor jooble
oilandgasjobsearchfocussed job listings for oul and gas industry
PetroplanVariety of G&G job related services available
working smartprovides listings of available consultants and also job searches
sub-surface-globalconsultancy link given here, other services on offer such as jobs listings.
rigzonejob listings
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Final Pentominoes Post: the code works !!

Probably two weeks have passed since the initial failure of the original code logic to find a solution to fit all 12 Pentominoes into a 12 by 5 space. After ironing out a few bugs in the initial code, it did manage to find solutions for 5,8,10 and one time 11 pieces. However, even after running overnight, it failed to find a solution to the full 12 piece problem. I think the code is sound, it’s just that it relies on chance to find a solution and with the large number of iterations required to solve for 12 pieces it is just very unlikely to randomly be selected. Eventually it should work – I might run this exe on an AWS cloud based PC which can easily be left to run for a week if required.

The following modifications in the logic resulted in success (and some very spaghetti like code.)

  1. The piece order can now be read in from data statements, and in the future can be made random. Normally I start off with the “X” pentomino since there are fewer possible starting solutions (this piece has no reflections or rotations).
  2. For a given starting position for piece1 the code evaluates all possible legal positions for piece2,3,4…and so on until no more solutions are found. It then moves back onto the next position of the previous piece until a full solution is found for all 12 pieces. This way ensures that the solutions tested run from left to right, so this algorithm has a kind of natural packing whilst still being a brute force search. If left to run “forever” this code should eventually find all 1010 possible solutions for the 12×5 fitting problem.

This version of the code has already produced two out of the 1010 solutions with the same starting position for the X piece. I’m happy that my initial goal has been achieved, within the timeframe assigned. Remaining tasks (which probably do not merit further posts) are:

  1. truly random piece order, starting with user decided starting piece.
  2. bring in piece reflections
  3. Only reflect or rotate pieces which need it (at the moment all pieces are rotated which is a bit wasteful.
  4. Simplify code logic and introduce more subroutines to reduce duplicated code.
  5. More advanced “hole checking” routines to reduce some spurious interim solutions
  6. Algorithm to weight solutions to proceed to faster convergence.
  7. Version which will find all possible solutions.
  8. Bring in some AI algorithms
  9. Recode in Python or something other than BASIC.

Watch this space for any progress reported !

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Diversions ….

I didn’t make much coding progress over the weekend, but I did find my 1975 copy of Martin Gardner’s book “Mathematical Puzzles and Diversions”. In the photo you can see a hexaflexagon that I constructed yesterday after reading this chapter of the book for the first time in over 40 years. Flexagons are well worth looking at, especially if you have 10 year old children. I found a few templates on the web with some interesting design ideas.

I also read the Polyominoes chapter, possibly for the first time. Since it was chapter nine I’m not sure that ever read it before..I seem to remember finding the book quite difficult to understand when I was 10. The Polynominoes piece is interesting, but the B&W graphics are really poor and rather uninspiring. I’m sure later books and versions of this text ( and its follow ups) had better graphics.

p.s. I found the book on a bookshelf in my house in Dublin, so no need to search through boxes of books in my loft in Mayo !

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Disappointing !!

Lots of progress in the past week, and quite a busy week, but no cigar as yet in terms of a full solution to the 12 piece pentominoes problem. The various modifications are summarised as follows.

  1. Using DATA statements to define each piece.

The use of data statements was a quicker way of defining each piece in terms of a 5×5 array. In the future then the piece can more easily be rotated and its edges can be automatically detected for fitting inside the chosen box. This modification was tested on the 5×5 test data.

  1. Rotating Each Piece using Matrix multiplication

Having defined each piece as a matrix, we can then use rotation of a matrix by 90 degrees to generate more possible pieces for each defined Pentomino. The logic used to rotate a matrix by 90 degrees was to take the matrix transpose (for which a function is already defined) and then swap matrix columns. I admit I found this solution on the internet, but I still havn’t used the internet to find possible solutions for the main Pentomino problem I’m trying to solve.

Finally I added some routines to remove spare rows and columns from the rotated matrix such that the Pentomino is always packed into the bottom left corner.

  1. Testing Solution on 5 pieces in 5×5 square

I had to change some small parts of the original logic, but the extension to rotating pieces worked well in terms of finding several additional solutions of this particular 5×5 problem.

Two such solutions are shown and generally less than 200 iterations were required.

  1. Extension to 12 pieces

The solution so far is restricted in that it doesn’t allow for reflections of the pieces, just rotations. The order of the pieces is fixed to either running from 1 to 12 or 12 to 1. However it still should be possible to find a solution. Since the end of the month was approaching, I quickly coded up the remaining 4 pieces and let the code iterate away at the entire problem I was trying to solve.

No solution found !! Disappointing !!

I think I left the code to run for 50,000 iterations before I gave up and tried it again. Still no joy. Then I found some small errors in defining the actual pieces, but each time I tried the code I obtained no solution. Unless there is a bug in the code, I’m pretty sure this brute force search should find one of the solutions …eventually…. but maybe I’m just not leaving it to run for long enough. Time for some thinking….

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Pentominoes: First Working Code

It works !! Moving on from the previous starting code.

  • I added a routine which would select one of the possible solutions from those available. All possible solutions are found and stored. Currently we select a solution for each piece randomly, later we might select the possible solutions one by one or high grade the solutions based on some algorithms we might define to obtain quicker convergence. At the moment once a solution is selected for a given piece, we move onto the next piece. If no solution is found for the next piece then we go back to the beginning again. A final solution, and associated graphics, is only produced once a solution is produced for all 5 pieces. Currently when we go back to the beginning we restart the searches each time and carry on with random selections. This is a bit wasteful, but it will work eventually.
  • I started with 3 pieces, with the first hard coded, and then checked the code such that solutions were found in the order 1,2,3 and 1,3,2. Next we freed up the first piece and tested orders 1,2,3 and 3,2,1. Ultimately all 12 pieces must be tested in random orders.
  • Next we made the code slightly slicker, and moved onto four pieces. Interestingly, despite previous testing, this uncovered a bug in which piece 3 found no solutions but the code could carry on and find a solution for piece 4. The logic had to be changed slightly to get around this problem resulting in some messy, but working code.
  • The final extension to 5 pieces was straightforward as was adding in the final screen graphics.

My 5 pieces are currently hard coded into orientations which I know will produce a solution for testing. The next level of complexity will be to add in rotations and reflections of the pieces. At the moment the piece shapes are hard coded – it would be possible to carry on with this method and hard code reflections and rotations for each piece. There are 63 possible combinations. I plan to investigate a more efficient way of storing the pieces in arrays and then using array manipulations to achieve the rotations where required. This will be the result of the next post.

Remember you can subscribe to the posts with a link to the right of the main post. I’m also experimenting linking these posts to my linkedin profile.

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Pentominoes: First Code Attempts

As I’ve mentioned, the actual coding is slightly ahead of the blog pages, because I’ve spent ages trying to configure the blog and the online Tonnta Store. All this while supervising two recalcitrant daughters for zoom school during covid lockdown.

I generally write code in chunks, testing each section and building in more detail. Well, I havn’t coded anything in 20+ years, so maybe I shouldn’t generalise ! The first code hardcodes the first piece, an “L” shape and runs a loop around a 5×5 box to fit in the second piece. Arrays are used to store both the solution and each piece with a trial being produced by adding the arrays together. There is code to check that the piece doesn’t fall outside of the array of the solution (in this case 5×5. I’m still thinking I might pad the solution area to avoid these checks, but then that would give me a much bigger search box which could be wasteful. I also wrote a text printing subroutine for debugging purposes since it would be quicker than the graphics shown earlier. The code cycles through possible solutions printing various diagnostic information together with the current position of the pieces. I used the wooden blocks that I bought to help visualise and check the various solutions that the code produced. In the above diagram the two pieces overlap (1+1)=2 so this would be rejected.

The next modification was a routine to check for isolated holes and thereby reject possible solutions. It searches around the potential hole (in this case top left) and if the hole is completely isolated then the potential solution is rejected. This is the first stage in “high grading” the possible piece positions. I’ve yet to decide whether this type, or further position grading will be required. It may be that too many checks will slow everything down – such a solution will be “found out” soon enough because the last pieces will ultimately not fit and the code will have to go back to the beginning anyway !

By the way, you can subscribe to this blog using the link to the right of the posts.

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More on Pentominoes

I was thinking about making a set of the 12 Pentominoes for my kids using salt dough or lego. However during lockdown we only have a few lego sets here and the pieces are tied up. I couldn’t bring myself to dismantle part of the Death Star for pieces, even though my daughters have removed most of the guns and fitted the Death Star out as bedrooms for Harry Potter lego minifigures. A few have commented on my linkedin post on different ways they have made Pentominoes in the past.

I found the following pictured game set online at Cogs the Brain Shop in Dublin. There are some quite nice things on the website and the delivery was fast, only a few days. My daughters went to work to find a solution…..and I was using the set to help visualise algorithms for my computer solution. Would we find a solution manually or my computer first ? The race was on…..

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As in all good projects, I decided to start with the final display, that is the graphics. I was able to locate the BBC microcomputer user guide in my loft. My guide is dated 1982 and acknowledges, among others, Richard Russell who wrote the BBCSDE interface that I decided to use in the previous post. The user guide contains a list of BBC BASIC commands and covers basic graphics with some sample programs including a classic Moon Lander game. I started by flicking through the book.

It didn’t take to long to write a simple BASIC code that would plot the grid and display Pentomino pieces in different colours. The code itself is quite useless, but it was a good start and will come in handy for displaying solutions (assuming I find any) and debugging algorithms that aim to fit the pieces together. I also found that the Teletext graphics mode contains several of the Pentomino pieces and that it is possible to define more as characters. An algorithm could probably be made directly using graphics commands and direct memory addressing or just based on the colours. However I decided against that approach since it would be difficult to port to other codes in the future.

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The Software Platform

This blog is already lagging a few days behind actual events, but that is probably of no consequence to the few readers likely to encounter it. Since I had decided to code in BBC basic, I was faced with two options

  1. Get the old BBC micro from the loft. I know it works, but it needs to be connected to a TV screen via a coaxial cable, so that’s marginally inconvenient to my TV watching family. Somewhere I have a 12″ B&W TV that I originally used for the BBC micro, but I’d have to find that. Also I’d have to get the floppy drive working. My DAD had a 512Kb hard disk, but I’ve never used that….all in all it seems a bit too retro even for a retro project like this.
  2. Use BeebEM – a PC based BBC emulator which I used in the past to play classic BBC games such as Elite. I had a little bit of a fiddle around with this and wrote a few lines of code. However it wasn’t easy to save the code in any kind of text file.

This is a screen shot of BeebEm running on Windows10 PC.

  1. Whilst searching around in BeebEm for something to save the code in a way I can use in other applications, I found BBCSDL a version of BBC basic for the PC ! This website is well worth checking out for a wealth of historical information and has been recently updated. The code window itself features two basic editors and can save the code as ASCII text (my original aim).

So, decision made, I decided to use BBCSDL to produce code.