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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>Hi, Rasmus, It’s great to hear from you. I wondered about that, although the way I conceived of it was different. What, I wondered, if they put a smaller Hampton maze inside the goal box of a Hampton maze. I would walk right by the entrance not matter if I had my whiskers on the right wall or the left. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Hi, Cody, Thanks for the tip <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal align=center style='text-align:center'>Nick<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nick Thompson<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Alexander Rasmus<br><b>Sent:</b> Saturday, February 27, 2021 6:43 PM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> Re: [FRIAM] solving mazes<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>Nick,<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Assuming that every intersection is 3-way isn't enough to guarantee that the maze is simply connected, see attached. If you put the exit in the no go region then the wall following strategy doesn't work, as entrance and exit won't be connected. <o:p></o:p></p></div><p class=MsoNormal><img border=0 width=240 height=320 style='width:2.5in;height:3.3333in' id="Picture_x0020_1" src="cid:image001.png@01D70D64.3A82CBA0"><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Best,<o:p></o:p></p></div><div><p class=MsoNormal>Alex<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Sat, Feb 27, 2021 at 5:10 PM cody dooderson <<a href="mailto:d00d3rs0n@gmail.com">d00d3rs0n@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><p class=MsoNormal>I am assuming this is a 2D maze. Wikipedia does a better job at explaining the problems with wall following than I can. <o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p style='mso-margin-top-alt:6.0pt;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;vertical-align:baseline;line-height:inherit'><i><span style='font-size:12.0pt;font-family:"Segoe UI",sans-serif;color:#202122'>If the maze is not simply-connected (i.e. if the start or endpoints are in the center of the structure surrounded by passage loops, or the pathways cross over and under each other and such parts of the solution path are surrounded by passage loops), this method will not reach the goal.</span></i><span style='font-size:12.0pt;font-family:"Segoe UI",sans-serif;color:#202122'><o:p></o:p></span></p><p style='mso-margin-top-alt:6.0pt;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;vertical-align:baseline;line-height:inherit'><span style='font-size:12.0pt;font-family:"Segoe UI",sans-serif;color:#202122'><o:p> </o:p></span></p></div><p class=MsoNormal style='margin-bottom:12.0pt'><o:p> </o:p></p><div><div><p class=MsoNormal>On Sat, Feb 27, 2021, 1:48 PM <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Hi, All, <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Due to a review I have been working on, I have been dragged back into thinking about maze learning in rats. Any animal I have ever known, when confined, will explore the boundaries of its enclosure. Cows, for instance will beat a path just inside the barbed wire that encloses them. So a maze is not only a series of pathways but it is also an enclosure. If the rat puts his left whisker against the left wall of the maze, he will eventually get to the goal box, right. It works with the Hampton Court Maze. On the second run, he can now use odor cues, such that any time he encounters his own odor both entering and leaving a passage way, he should just skip that passage way. <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>So I am wondering, you topologists (??) out there, how general is the statement, “every maze is an enclosure” and what is the limitation on the idea that any maze can be solved by putting your right or left hand on a wall and continuing to walk until you find the goal or are let out of the maze. Now I should quickly say that rat mazes are usually composed of a series of bifurcating choice points, where the rat can go either left or right. Some choices lead ultimately to dead ends. In sum, a runway in such a maze can go straight, turn R or L without choice or form a T with a right or left choice. My intuition is that no such maze can be designed that does not permit the boundary following strategy. <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Nick <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Nick Thompson<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="mailto:ThompNickSon2@gmail.com" target="_blank">ThompNickSon2@gmail.com</a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://wordpress.clarku.edu/nthompson/" target="_blank">https://wordpress.clarku.edu/nthompson/</a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div><p class=MsoNormal>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><o:p></o:p></p></blockquote></div></div><p class=MsoNormal>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><o:p></o:p></p></blockquote></div></div></body></html>