{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Intro","Ant","Lesson"],"not_rendered":{"charts":0,"images":3,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Intro","index":0,"n_rows":67,"n_cols":15,"rows_kept":67,"cut":false,"hidden":false,"merged":[]}
["Humberto Barreto",null,null,null,null,"You must ENABLE MACROS (see below for details) when you open this file.",null,null,null,null,null,null,null,null,"2021-07-22"]
["hbarreto@depauw.edu"]
[]
["Langton's ant follows two simple rules to move around, yet remarkably it produces something ordered."]
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["As of this writing,  it seems that no matter the initial grid, the ant will eventually build a highway (this mysterious term, which you will discover as you learn about Langton's ant, is an open-problem that is the subject of current research)."]
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["Langton's ant is on a plane with black and white squares. The ant can be facing north, south, east, or west. It follows these two rules, then moves forward:"]
[null,"1) If it is on a white square, it turns right; else (it is on a black square), it turns left."]
[null,"2) The ant moves forward one square (in the direction it is facing) and the square it was on flips color."]
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["A spreadsheet is the perfect place to implement Langton's ant. Enter a greater than sign, > (representing the ant facing east), in cell B13 below."]
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[]
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["We can easily color a cell black (white is the default background color). Click cell C14 and then click the Fill Color button (the bucket in the Font group) to make it black."]
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["Moving the ant is a little trickier. We will do it manually, applying the two rules, to see how it works."]
["At B13, the ant is on a white square so, following the first rule, it will turn right, becoming a v."]
["Following the second rule, it will move forward one square, down to cell B14, and the square it was on (B13) flips to black."]
["The ant is now in cell B14 and facing south so enter the letter v in cell B14."]
["Delete the > character in cell B13 and change the cell color to black to finish applying the second rule."]
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["This is what cells B13:D15 should look like (if you followed the instructions above):"]
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[]
[]
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["Can you walk through what the next move will be?"]
["It is on a white square, so it turns left to <, then it hops to cell A14 and cell B14 flips to black."]
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["Moving the ant manually quickly becomes tedious. We can automate the process with Excel's programming language, Visual Basic."]
["This workbook has macros that will enable Langton's ant to move by following the two simple rules."]
[null,"It is not necessary, but if you want to see the code, press alt+F11 on your keyboard (or right-click the Intro sheet tab at the bottom left of this window and select View Code)."]
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["Read the instructions below before you play with Langton's ant in the Ant sheet. "]
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["When you go to the Ant sheet, you will see a controller floating above the screen (see below if you do not see this when you go to the Ant sheet). "]
["Use the controller to move the ant around. Your goal is to generate the highway and understand what it means."]
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["When you first arrive at the Ant sheet, add an ant (enter <, >, v, or ^ in any cell) and have it follow the two simple rules to move around."]
[null,"Click the Move One Step button a few times to confirm that the ant is moving as expected, following the two rules."]
[null,"To be able to see the direction the ant is facing, we use yellow instead of black as our non-white cell fill color."]
[null,"Try the Many Steps button with a few hundreds steps."]
[null,"If you click the check box, the macro runs much faster because it does not have to show each step. It computes the path and then displays it."]
[]
[null,"Starting from a completely white grid, Langton's ant starts to build the highway mentioned above around 10,000 steps (OK, the 9,978th step, to be exact)."]
[null,"To see the highway clearly, you need to run around 11,000 steps (starting from a blank grid)."]
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[null,"After you confirm that the ant builds a highway, click the Reset button and create other grid patterns by filling some cells with yellow and then adding the ant and using the buttons to move around."]
[null,"You can try typical geometric shapes (for example, a triangle) or a random smattering of yellow cells."]
[null,"Do you find any interesting results?"]
[null,"Does the ant ever fail to build the highway? That would be a BIG deal."]
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[null,"After you are finished, take a look at the Lesson sheet to make sure you understand a key idea demonstrated by Langton's ant."]
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["Proceed to the Ant spreadsheet and explore the properties and patterns of Langton's ant!"]
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[]
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["Software Requirements:"]
[null,"You need \"desktop\" (not online) Microsoft Excel, Windows version 2007 or greater to get full functionality from this file."]
[null,null,"This file can be opened with Mac Excel, but it uses Visual Basic code that may not be fully supported on a Mac. "]
[null,null,"Online Excel can open this file, but none of the macros will run. You need to have Excel on your computer and open this file with your Excel application."]
[null,"You must be sure to Enable Content or the buttons and code in this macro-enabled workbook will not work."]
[null,null,"If you opened this workbook and did not enable macros, close it, open it again, and click the Enable Content button -->"]
[null,null,"Search \"enable macros\" in Excel's Help for more information on how to do this."]

{"sheet":"Ant","index":1,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Lesson","index":2,"n_rows":26,"n_cols":16,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
["This video shows that many more patterns can be produced by extending the rules:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"After 11,000 steps, starting from a blank grid, and \"<\":"]
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["https://www.youtube.com/watch?v=1X-gtr4pEBU"]
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["A key idea is that Langton's ant produces patterns and order even though it is just following two rules."]
["This is called emergent behavior."]
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["Langton's ant shows that when we see a pattern, it may be the result of underlying individual decisions and interactions."]
["There are many, many applications of this key idea."]
["Geese that fly long distances arrange themselves in a V-pattern not because a leader tells them what to do, but because each bird seeks to minimize effort."]
["In Economics, patterns that emerge from the interactions of individuals are said to be produced by an invisible hand and generate a spontaneous order."]
["In Mathematics and Computer Science, this is called self-organization."]
[]
["Langton's ant makes clear that individuals may be doing something really simple, yet the overall result can be complex and ordered."]
["This is counter-intuitive because we usually think that something complicated must require conscious, planned, and sophisticated intention."]
["It is true that we can create something by design (like a car or the Mona Lisa), but do not forget that Langton's ant can make a highway!"]
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["For more, click on the link below:"]
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["https://www.google.com/search?q=langton%27s+ant"]
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["If you like this, you might like "]
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["Professor Stewart's Cabinet of Mathematical Curiosities (2009)"]
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["This book discusses Langton's Ant on pp. 141-143 and says something you might have stumbled across in your explorations:"]