tag:blogger.com,1999:blog-19303585.post8906609218779679751..comments2019-01-18T18:02:33.010+00:00Comments on John Graham-Cumming: More fun with toys: the Ikea LILLABO Train SetJohn Graham-Cummingnoreply@blogger.comBlogger46125tag:blogger.com,1999:blog-19303585.post-60378868700209083772015-09-13T20:14:38.615+00:002015-09-13T20:14:38.615+00:00I'm quite happy with the overview of the 23! I...I'm quite happy with the overview of the 23! I noticed your code, but it would take me quite some time to install and understand. Thank you.<br /><br />About http://i.imgur.com/r2X0UzT.png. You write "In my layouts I allowed swapping of the bridge and two straights and considered them the same layout." With this criterion, yes, they are identical. Ultimately, it's a matter of taste. <br /><br />Please, note that in all the other original layouts, swapping the bridge with the two straights can be done by a geometric transformation of the layout: taking a mirror image or a rotation or a combination. (Yes, you will need both sides of the tracks.) But only in this layout, you actually have to switch them. So, that's why I thought that you "missed" it.<br /><br />Thank you for following up with your questions. I realize you had a different goal with your original program.<br /><br />Cuc.cuchttps://www.blogger.com/profile/16261087995269274220noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-81678960710726134452015-09-12T08:32:00.955+00:002015-09-12T08:32:00.955+00:00@cuc
I published the code to draw the layouts her...@cuc<br /><br />I published the code to draw the layouts here: http://blog.jgc.org/2010/01/ikea-lillabo-processing-code.html but to save you the time I put all the layouts you had found (23 of them including my 9) and here's the picture of that: http://i.imgur.com/Cjm9l9T.png<br /><br />You say that ACAAAAACSSAAAAB is missing from my layouts. Here's a picture of it: http://i.imgur.com/r2X0UzT.png<br /><br />For ease of comparison here's yours and mine together: http://i.imgur.com/Sc1ckNo.png Now we get into a question of whether these two are different. In my layouts I allowed swapping of the bridge and two straights and considered them the same layout. Also the tracks are double sided so it's possible to transform your layout into mine by flipping it over.<br /><br />So I'm not sure yours is totally different to mine. Thoughts?<br /><br />John Graham-Cumminghttps://www.blogger.com/profile/12998100764952319513noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-11720556436572999072015-09-12T08:00:40.425+00:002015-09-12T08:00:40.425+00:00@John,
you're right, the longer list does no...@John, <br /><br />you're right, the longer list does not contain any new designs with the Bridge in a different place. It contains all possible layouts with the bridge in one piece or used as two separate pieces (remember the slot-car racing tracks, for which it is really all the other designs that do not form a problem, but only the figure-8 needs strutting.) So, there are 14 alternative designs. I would like to see pictures of them. I tried with primitive means (Windows Paint), but the results don't look presentable. I am thinking of making a paper model of the tracks and taking pictures . . . <br /><br />Just to be sure you understood, note that by changing the bridge in<br />AAAASSACAAAAACB, we get <br />ACAAAAACSSAAAAB, which was missing from your layouts.<br /><br />Yours, Cuc.<br /><br />cuchttps://www.blogger.com/profile/16261087995269274220noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-48395652414619800852015-09-09T09:18:28.935+00:002015-09-09T09:18:28.935+00:00@cuc. It's absolutely the case that if you tre...@cuc. It's absolutely the case that if you treat the bridge as two piece you get more layouts. This was not in my original plan as it requires supports for the parts that are between the two bridge parts.<br /><br />I don't see any new layouts where the bridge is treated as a single item. Do you?John Graham-Cumminghttps://www.blogger.com/profile/12998100764952319513noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-49242450392115236072015-09-09T09:02:35.943+00:002015-09-09T09:02:35.943+00:00Hi John,
I couldn't wait on your program'...Hi John, <br /><br />I couldn't wait on your program's output :-P. So, I scrutinized my list by hand and the following 23 designs remained (no rotations or mirror images):<br /><br />Final list - Total layouts: 23.<br />Of these 23, 3 are the independents (AA,BB and CC), and the other 20 are modified doughnuts (adding 4 straights in various places). Layouts marked * were found by you and allow the whole bridge in one or two positions (B=SS).<br /><br />S = Straight, A = Anticlockwise curve, C = Clockwise curve<br /><br />AA. [SSAAAAAASSCCCCCC] - figure 8<br />01. [SSAAAAACSSAAAAAC]*<br />02. [SSAAAACASSAAAACA]*<br />BB. [SSAAAACCAAAASSAA] - figure L<br />03. [SSAAAASACSAAAAAC]*<br />04. [SSAAAASCASAAAACA]*<br />05. [SSAAAASSACAAAAAC]*<br />06. [SSAAACAASSAAACAA]*<br />CC. [SSAAACAACAAASSAA] - figure M<br />07. [SAAAAACSASAAAASC]<br />08. [SAAAAASCSAAAAASC]<br />09. [SAAAACSASAAAACSA]<br />10. [SAAAACSASAAASACA]<br />11. [SAAAASACSAAAASAC]<br />12. [SAAACASASAAACASA]<br />13. [SAAACASASAAASCAA]<br />14. [SAAACSAASAAACSAA]<br />15. [SAAACSAASAASACAA]<br />16. [SAAASAACSAAASAAC]<br />17. [SAAASACASAAASACA]<br />18. [SAAASASCAAAAACSA]<br />19. [SAACAASASAACAASA]<br />20. [SAACASAASAACASAA]<br /><br />I hope you'll verify my list (did I miss anything?) and make the accompanying pictures for easy reference. In the mean time, these 23 designs can be a lot of fun to build.<br />In fact, there are a few more designs which do not use all available tracks.<br /><br />[AAAAAAAA] - circle<br />[AAAASAAAAS] - small ellipse<br />[AAAASSAAAASS] - ellipse<br />[AAASASAAASAS] - diamond<br />[AASAASAASAAS] - square<br />[AAAA.AC.AAAA.AC] - doughnut<br /><br />Modifying the doughnut gives a number of other designs by adding only 2 straights. To get these, take any doughnut design in the list above, and remove two parallel straights between which are at least 4 A's. For some designs this gives as much as 4 derivative layouts using only 2 straights. I did not yet determine all these designs, but for any practical purposes I consider them included . . .<br /><br />Enjoy your day,<br />Cuccuchttps://www.blogger.com/profile/16261087995269274220noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-41672310017348816612015-09-09T02:56:57.664+00:002015-09-09T02:56:57.664+00:00Dear John,
I was looking for exactly this kind o...Dear John, <br /><br />I was looking for exactly this kind of problem. Doing some of my own research, I found more than 9 layouts, in fact I found 104. These haven't been checked on doubles, and consider the bridge to be two straights. Nevertheless, I think your list of 9 is not complete. I will give a missed layout at the end of this post. But to introduce you to the error I see, consider the track coded by:<br /><br />AAAA.AC.AAAA.AC <br /><br />(I call it a doughnut for lack of a better word, periods are only for style)<br />I noted that each connection point has a certain angle, and for each angle there are either 2 or 4 parallel points.<br /><br />Your solutions 1, 2 and 6 in the picture are not derived from this doughnut. I'd like to call them "independents". Interestingly, design no.6 in the picture was new to me! <br /><br />All other layouts are derived from the doughnut by introducing the bridge at a certain connection point. To avoid doubles, we only have to put the bridge in the beginning of the string, and place the two other straights elsewhere on parallel connection points.<br /><br />Yours (minus the three "independents"):<br />1. CAAAAACASSAAAAB<br />2. CAAAAASCASAAAAB<br />3. CAAAAASSCAAAAAB<br />4. ACAAAASACSAAAAB<br />5. ACAAAASSACAAAAB<br />6. AACAAASSAACAAAB<br /><br />Mine on the left and your corresponding to the right (in reverse)<br />BAAAASS.AC.AAAA.AC = 1. CAAAAACASSAAAAB<br />BAAAAS.AC.SAAAA.AC = 2. CAAAAASCASAAAAB<br />BAAAA.AC.SSAAAA.AC = 3. CAAAAASSCAAAAAB<br />ABAAA.ASSC.AAAA.AC = ACAAAAACSSAAAAB missing<br />ABAAA.ASC.ASAAA.AC = 4. ACAAAASACSAAAAB<br />ABAAA.AC.ASSAAA.AC = 5. ACAAAASSACAAAAB<br />AABAA.AC.AASSAA.AC = 6. AACAAASSAACAAAB<br />AAABA.AC.AAASSA.AC = 6. AACAAASSAACAAAB<br />AAAAB.AC.AAAASS.AC = 5. ACAAAASSACAAAAB<br />AAAAB.AC.AAAAS.ACS = 4. ACAAAASACSAAAAB<br />AAAAB.AC.AAAA.ACSS = ACAAAAACSSAAAAB missing (same as above)<br />AAAA.ABC.AAAA.ASSC = 3. CAAAAASSCAAAAAB<br />ASAAA.ABC.AAAA.ASC = 2. CAAAAASCASAAAAB<br />ASSAAA.ABC.AAAA.AC = 1. CAAAAACASSAAAAB<br /><br />The unidentified layout would be similar to 1. (listed here) but with the bridge and straight tracks interchanged (it's the only one that is a non-symmetrical)<br />--<br />Also, as noted, there are many more designs if you allow the bridge to be taken apart. The tracks in between can be easily strutted. Note that we can consider the identical problem with kart track layouts. With kart tracks it is the bridge that needs "struts" only in the figure 8 and in all other designs counts as 2 straights. So, it is natural to consider the bridge to be two "straights" as well. Alternatively, solve it for the simple kart layouts (http://ow.ly/RXCkG at Amazon).<br />--<br />In this post, I showed that your program has a "bug" (it did not produce all possible layouts modulo symmetry and rotation).<br />--<br />I also learned how to identify layouts written in different ways, by considering the Bridge to be "the first piece" and looking for the layout clockwise or anticlockwise which has the most A's following it.<br />--<br />I indicated that the bridge can be thought of as two straights. This will give more designs not shown. I am curious to see these other layouts (strutted in case of train set, flat in case of kart race set).<br />--<br />Thank you so much.cuchttps://www.blogger.com/profile/16261087995269274220noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-38170211559951750872013-06-09T11:30:33.530+00:002013-06-09T11:30:33.530+00:00A great post. This train set has been available fo...A great post. This train set has been available for decades and is still being sold today.<br /><br />However I don't quite understand why you made your program so complicated, instead of just looping through all the combinations/permutations? Was this so it would run faster? Did you add bits as you tried it out?<br /><br />John Smithhttps://www.blogger.com/profile/06217771463909130309noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-77187614603330936662013-02-15T13:17:47.778+00:002013-02-15T13:17:47.778+00:00@James. Glad all this blogging is helping people!@James. Glad all this blogging is helping people!John Graham-Cumminghttps://www.blogger.com/profile/12998100764952319513noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-36726577780313806212013-02-15T12:17:50.192+00:002013-02-15T12:17:50.192+00:00Mr Make - this is probably the most serindiptous d...Mr Make - this is probably the most serindiptous day. In one day I had to make a quirky trick to a makefile and recall from your Mr Make contributions to CMCrossroads that you had a reference model solution to my makefile requirement (then discovered your self published book on make and purchased a copy.) Then, midday, I had a question in regards to high altitude GPS with our Telit modem and found your article on the GAGA-1. Now, after my 2.5 year old received her expansion pack for Lillabo, I was curious to see what ways it could be mapped out into a complete circuit and discovered this article. Google seems to be ranking you well for all sorts of eclectic searches.James Hanleyhttps://www.blogger.com/profile/16907182483657152095noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-1154815062542414092013-02-15T12:17:30.868+00:002013-02-15T12:17:30.868+00:00Mr Make - this is probably the most serindiptous d...Mr Make - this is probably the most serindiptous day. In one day I had to make a quirky trick to a makefile and recall from your Mr Make contributions to CMCrossroads that you had a reference model solution to my makefile requirement (then discovered your self published book on make and purchased a copy.) Then, midday, I had a question in regards to high altitude GPS with our Telit modem and found your article on the GAGA-1. Now, after my 2.5 year old received her expansion pack for Lillabo, I was curious to see what ways it could be mapped out into a complete circuit and discovered this article. Google seems to be ranking you well for all sorts of eclectic searches.James Hanleyhttps://www.blogger.com/profile/16907182483657152095noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-38451441086700339892013-01-14T20:27:01.183+00:002013-01-14T20:27:01.183+00:00I have the exact same question as Krystal! I can&...I have the exact same question as Krystal! I can't get the track to make a complete loop using all the bits from the extension pack, nor can I find anywhere online to show me how...A(me)https://www.blogger.com/profile/06407417460797812800noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-61801388184455491342012-12-26T22:03:46.644+00:002012-12-26T22:03:46.644+00:00Hello I am hoping you can help me. My son has had ...Hello I am hoping you can help me. My son has had the 20 piece set for a while and for Christmas we got him the 10 piece set as an addition. Can you post some ways to build with all 30 pieces?Krystalhttps://www.blogger.com/profile/03470037022238756036noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-32655836725252339302012-12-26T22:02:28.631+00:002012-12-26T22:02:28.631+00:00Hello I was wondering if you could help. I bought ...Hello I was wondering if you could help. I bought my son the 20 piece set a while back and just added the 10 piece set to it. Can you post some ways to build with that? I am no good at Krystalhttps://www.blogger.com/profile/03470037022238756036noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-34585377887893087832012-05-13T15:20:52.409+00:002012-05-13T15:20:52.409+00:00Hi John, this code is great but it doesn't tak...Hi John, this code is great but it doesn't take into account when the track overlaps it self. <br /><br />As is it will generate many impossible tracks like AAAASAAAAAAAASAAAAB.<br /><br />I'm trying to improve it but I'm not a native perl developer.nmfnhttps://www.blogger.com/profile/08639989676791117135noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-63481304230491119972012-02-18T19:36:28.263+00:002012-02-18T19:36:28.263+00:00This is great- we just bought the train set yester...This is great- we just bought the train set yesterday. I think we will have to go back to Ikea to get a few more tracks to play with.Meaghanhttps://www.blogger.com/profile/07226280837097124589noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-62053807209884480112012-01-23T12:33:23.839+00:002012-01-23T12:33:23.839+00:00Love it! Now to go and make them all with my toddl...Love it! Now to go and make them all with my toddler.Louisehttps://www.blogger.com/profile/13786434091149092927noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-55540186611572450402011-12-29T18:07:18.562+00:002011-12-29T18:07:18.562+00:00The code on this page is written in Perl: it calcu...The code on this page is written in Perl: it calculates the track layouts. Drawing the layouts was made using a Processing program here: http://blog.jgc.org/2010/01/ikea-lillabo-processing-code.htmlJohn Graham-Cumminghttps://www.blogger.com/profile/12998100764952319513noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-79448273324317525012011-12-27T12:01:37.702+00:002011-12-27T12:01:37.702+00:00What version of Processing did you used? I downloa...What version of Processing did you used? I downloaded the latest (1.5.1 for Windows, from here: http://processing.org/download/) and it complains about everything: about ' characters, comments and actually their source code looks a bit different than yours (for example functions are defined like "void myfunc() {}).Igor Bljahhinhttps://www.blogger.com/profile/17460618073449065722noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-9379719684430663092011-05-22T17:58:24.316+00:002011-05-22T17:58:24.316+00:00Hello. Whould you like to share the code to genera...Hello. Whould you like to share the code to generate the images?Gustavo Felisbertohttps://www.blogger.com/profile/06109821199921075583noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-47930320456929760932010-04-23T01:32:45.554+00:002010-04-23T01:32:45.554+00:00Very impressive bit of programming. I was searchin...Very impressive bit of programming. I was searching track designs before purchasing the set. Where did you find a 20 piece set? The current Ikea sets ( http://www.ikea.com/us/en/search/?query=lillabo ) are a 3 piece train set, a 12 piece bridge & tunnel set with only strait pieces, and a 10 piece 'rail' set that includes 4 curves, 2 short straight, 2 long straight and 2 Vs or forks (with which you can't even make a loop with). So are you telling me I would need to purchase 2, 10 piece sets just to make a circle?Jackihttps://www.blogger.com/profile/07268496204845354649noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-86078974023938281262010-01-26T05:53:24.381+00:002010-01-26T05:53:24.381+00:00I am saddened to see that there is only one layout...I am saddened to see that there is only one layout that uses the bridge to go over another peice of track. Does adding peices increase the number of bridge over track configurations?liquidhttps://www.blogger.com/profile/07128447848317290773noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-43502482418870245832010-01-16T06:57:52.531+00:002010-01-16T06:57:52.531+00:00That's awesome. Wondering if you would alter ...That's awesome. Wondering if you would alter your program to see what combinations you could get with double the pieces. My kids got two sets last Christmas and we spend tons of times improvising new setskalisurferhttps://www.blogger.com/profile/04857640395519430421noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-6755467699277860232010-01-15T23:35:39.940+00:002010-01-15T23:35:39.940+00:00This brings back memories. I had a set just like t...This brings back memories. I had a set just like this 25 years ago, not from ikea though obviously!acme01https://www.blogger.com/profile/15795763787458277282noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-91071617428473156152010-01-08T16:33:33.657+00:002010-01-08T16:33:33.657+00:00Amazing! I am very curious to know how long did it...Amazing! I am very curious to know how long did it take you to write the code?damianhttps://www.blogger.com/profile/14022629326485694288noreply@blogger.comtag:blogger.com,1999:blog-19303585.post-90869679196372294332010-01-08T15:02:58.351+00:002010-01-08T15:02:58.351+00:00http://mathforum.org/library/drmath/view/52573.htm...http://mathforum.org/library/drmath/view/52573.htmlshawndumashttps://www.blogger.com/profile/01372569176363474336noreply@blogger.com