(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2685062, 64195]*) (*NotebookOutlinePosition[ 2699189, 64515]*) (* CellTagsIndexPosition[ 2696435, 64453]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Automata Containing Evolutionary Algorithms: Behavior and Learning Under \ Law\ \>", "Title", CounterAssignments->{{"Subtitle", 1}}], Cell["\[Copyright] Seth J. Chandler and Christian J. Jacob 1999", "Copyright"], Cell[TextData[{ "Chapter ", CounterBox["Subtitle"], ": Actual Experiments" }], "Subtitle"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell["\<\ In this notebook, we attempt to explore and validate the tools developed in \ the first chapter for examining the behavior of cellular automata containing \ genetic programs. The idea is not to exhaustively catalog the results of all \ permutations of the types of experiments permitted by the tools, but rather \ to demonstrate the sort of experiments made possible them. We hope these \ initial forays yield insight into the evolution of economic behavior and \ learning.\ \>", "Text"], Cell["\<\ Note: The paper shown here is an abridged version of a more complete \ Mathematica notebook available on request from Professor Chandler at \ SChandler@uh.edu. Supporting code such as work on genetic operators is also \ available.\ \>", "SmallText"] }, Closed]], Cell[CellGroupData[{ Cell["Auxilliary Functions Needed for Visualization", "Section"], Cell["\<\ We begin by creating some auxilliary functions needed to assist in \ visualization and analysis of the experiments in which we evolve automata \ containing evolutionary algorithms. \ \>", "Text"], Cell["\<\ An abridged version of this paper will not contain the code for these \ functions.\ \>", "SmallText"], Cell["\<\ Part of the code in this section is adapted from the standard package, \ DiscreteMath`Combinatorica. (Skienna, 199x).\ \>", "SmallText"] }, Closed]], Cell[CellGroupData[{ Cell["Experiments", "Section"], Cell[CellGroupData[{ Cell["\<\ Baseline: Harmless Cows, No Computation Costs, No Recombination and No \ Exogenous Mutations\ \>", "Subsection"], Cell[TextData[{ "The auxilliary tools are now created with which to explore the evolution \ of the economy. As a first attempt, we use the code below in Code Fragment ", CounterBox["NumberedInput", "myinitialconditions"], " to create an economy with fifteen sites. We start with an economy in \ which no recombination occurs. Initial prices are set (arbitrarily) at 6 and \ 5." }], "Text"], Cell[BoxData[ \(myinitialconditions = initialcondition[15, nolearning, {6. , 5. }]; \)], "NumberedInput", CellTags->"myinitialconditions"], Cell[TextData[{ "We then use the code shown in Code Fragment ", CounterBox["NumberedInput", "baseline"], " to ", "evolve this economy over 20 additional iterations. By setting the \"death \ criteria\" function equal to False, we prevent any exogenous mutations of the \ sites. We assume that ranchers pay damages based on the proportion of harm \ they cause neighboring farmers and that farmers receive all sums paid by \ ranchers. We render cows harmless by setting the damage factor from cows \ equal to 0.0. Finally, we assume computation costs are equal to 0. This \ experiment provides us with a baseline against which to measure the effect of \ other factors. It also creates a simple test of our tools' functionality." }], "Text"], Cell[BoxData[ \(baseline = \(evolutionList[ process[tc, Identity, proportionaldamages, 0 &, Function[1 &], Function[False], rs, 0. , verbose \[Rule] False]]\)[ myinitialconditions, 20]; \)], "NumberedInput", CellTags->"baseline"], Cell["\<\ On an average computer,this takes on the order of ten seconds. We often store \ the data in a file for later analysis.\ \>", "SmallText"], Cell["\<\ We can check to see that our economy ends up matching our automatonPattern, \ which is evidence that the program has operated successfully.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(MatchQ[Last[baseline], automatonPattern]\)], "NumberedInput"], Cell[BoxData[ \(True\)], "Output"] }, Closed]], Cell[TextData[{ "We can visualize the economic history here in several ways. In Figure ", CounterBox["NumberedFigure", "baselinelandscape"], ", we look at behaviors over time. Areas that are green denote farming \ while areas that are red denote ranching. 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(either farming or ranching). A landscape produced at \ random would tend to have a clustering level of 0.25. A well organized \ clustered landscape would tend to have a clustering level close to ", Cell[BoxData[ \(TraditionalForm\`\(q - 2 \((c - 1)\)\)\/q\)]], " where q is the length of the landscape (15) and c is the size of the \ cluster (3). Thus for our landscape of 15 sites with a cluster length of \ three, perfect clustering would yield about 0.73. 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-1.25 Mabsadd L .64286 .60332 2.165 -1.25 Mabsadd L .64286 .60332 0 2.5 Mabsadd L closepath F .69048 .55623 0 2.5 Mabsadd m .69048 .55623 -2.165 -1.25 Mabsadd L .69048 .55623 2.165 -1.25 Mabsadd L .69048 .55623 0 2.5 Mabsadd L closepath F .7381 .60332 0 2.5 Mabsadd m .7381 .60332 -2.165 -1.25 Mabsadd L .7381 .60332 2.165 -1.25 Mabsadd L .7381 .60332 0 2.5 Mabsadd L closepath F .78571 .55623 0 2.5 Mabsadd m .78571 .55623 -2.165 -1.25 Mabsadd L .78571 .55623 2.165 -1.25 Mabsadd L .78571 .55623 0 2.5 Mabsadd L closepath F .83333 .60332 0 2.5 Mabsadd m .83333 .60332 -2.165 -1.25 Mabsadd L .83333 .60332 2.165 -1.25 Mabsadd L .83333 .60332 0 2.5 Mabsadd L closepath F .88095 .55623 0 2.5 Mabsadd m .88095 .55623 -2.165 -1.25 Mabsadd L .88095 .55623 2.165 -1.25 Mabsadd L .88095 .55623 0 2.5 Mabsadd L closepath F .92857 .60332 0 2.5 Mabsadd m .92857 .60332 -2.165 -1.25 Mabsadd L .92857 .60332 2.165 -1.25 Mabsadd L .92857 .60332 0 2.5 Mabsadd L closepath F .97619 .55623 0 2.5 Mabsadd m .97619 .55623 -2.165 -1.25 Mabsadd L .97619 .55623 2.165 -1.25 Mabsadd L .97619 .55623 0 2.5 Mabsadd L closepath F 0 g .001 w [ .5 3 ] 0 Mabsdash .02381 .37965 m .07143 .39142 L .11905 .20307 L .16667 .0618 L .21429 .0618 L .2619 .01472 L .30952 .10889 L .35714 .01472 L .40476 .10889 L .45238 .01472 L .5 .10889 L .54762 .01472 L .59524 .10889 L .64286 .01472 L .69048 .10889 L .7381 .01472 L .78571 .10889 L .83333 .01472 L .88095 .10889 L .92857 .01472 L .97619 .10889 L s 1 0 0 r .0001 w [ ] 0 setdash .02381 .37965 -2.5 2.5 Mabsadd m .02381 .37965 2.5 2.5 Mabsadd L .02381 .37965 2.5 -2.5 Mabsadd L .02381 .37965 -2.5 -2.5 Mabsadd L .02381 .37965 -2.5 2.5 Mabsadd L closepath F .07143 .39142 -2.5 2.5 Mabsadd m .07143 .39142 2.5 2.5 Mabsadd L .07143 .39142 2.5 -2.5 Mabsadd L .07143 .39142 -2.5 -2.5 Mabsadd L .07143 .39142 -2.5 2.5 Mabsadd L closepath F .11905 .20307 -2.5 2.5 Mabsadd m .11905 .20307 2.5 2.5 Mabsadd L .11905 .20307 2.5 -2.5 Mabsadd L .11905 .20307 -2.5 -2.5 Mabsadd L .11905 .20307 -2.5 2.5 Mabsadd L closepath F .16667 .0618 -2.5 2.5 Mabsadd m .16667 .0618 2.5 2.5 Mabsadd L .16667 .0618 2.5 -2.5 Mabsadd L .16667 .0618 -2.5 -2.5 Mabsadd L .16667 .0618 -2.5 2.5 Mabsadd L closepath F .21429 .0618 -2.5 2.5 Mabsadd m .21429 .0618 2.5 2.5 Mabsadd L .21429 .0618 2.5 -2.5 Mabsadd L .21429 .0618 -2.5 -2.5 Mabsadd L .21429 .0618 -2.5 2.5 Mabsadd L closepath F .2619 .01472 -2.5 2.5 Mabsadd m .2619 .01472 2.5 2.5 Mabsadd L .2619 .01472 2.5 -2.5 Mabsadd L .2619 .01472 -2.5 -2.5 Mabsadd L .2619 .01472 -2.5 2.5 Mabsadd L closepath F .30952 .10889 -2.5 2.5 Mabsadd m .30952 .10889 2.5 2.5 Mabsadd L .30952 .10889 2.5 -2.5 Mabsadd L .30952 .10889 -2.5 -2.5 Mabsadd L .30952 .10889 -2.5 2.5 Mabsadd L closepath F .35714 .01472 -2.5 2.5 Mabsadd m .35714 .01472 2.5 2.5 Mabsadd L .35714 .01472 2.5 -2.5 Mabsadd L .35714 .01472 -2.5 -2.5 Mabsadd L .35714 .01472 -2.5 2.5 Mabsadd L closepath F .40476 .10889 -2.5 2.5 Mabsadd m .40476 .10889 2.5 2.5 Mabsadd L .40476 .10889 2.5 -2.5 Mabsadd L .40476 .10889 -2.5 -2.5 Mabsadd L .40476 .10889 -2.5 2.5 Mabsadd L closepath F .45238 .01472 -2.5 2.5 Mabsadd m .45238 .01472 2.5 2.5 Mabsadd L .45238 .01472 2.5 -2.5 Mabsadd L .45238 .01472 -2.5 -2.5 Mabsadd L .45238 .01472 -2.5 2.5 Mabsadd L closepath F .5 .10889 -2.5 2.5 Mabsadd m .5 .10889 2.5 2.5 Mabsadd L .5 .10889 2.5 -2.5 Mabsadd L .5 .10889 -2.5 -2.5 Mabsadd L .5 .10889 -2.5 2.5 Mabsadd L closepath F .54762 .01472 -2.5 2.5 Mabsadd m .54762 .01472 2.5 2.5 Mabsadd L .54762 .01472 2.5 -2.5 Mabsadd L .54762 .01472 -2.5 -2.5 Mabsadd L .54762 .01472 -2.5 2.5 Mabsadd L closepath F .59524 .10889 -2.5 2.5 Mabsadd m .59524 .10889 2.5 2.5 Mabsadd L .59524 .10889 2.5 -2.5 Mabsadd L .59524 .10889 -2.5 -2.5 Mabsadd L .59524 .10889 -2.5 2.5 Mabsadd L closepath F .64286 .01472 -2.5 2.5 Mabsadd m .64286 .01472 2.5 2.5 Mabsadd L .64286 .01472 2.5 -2.5 Mabsadd L .64286 .01472 -2.5 -2.5 Mabsadd L .64286 .01472 -2.5 2.5 Mabsadd L closepath F .69048 .10889 -2.5 2.5 Mabsadd m .69048 .10889 2.5 2.5 Mabsadd L .69048 .10889 2.5 -2.5 Mabsadd L .69048 .10889 -2.5 -2.5 Mabsadd L .69048 .10889 -2.5 2.5 Mabsadd L closepath F .7381 .01472 -2.5 2.5 Mabsadd m .7381 .01472 2.5 2.5 Mabsadd L .7381 .01472 2.5 -2.5 Mabsadd L .7381 .01472 -2.5 -2.5 Mabsadd L .7381 .01472 -2.5 2.5 Mabsadd L closepath F .78571 .10889 -2.5 2.5 Mabsadd m .78571 .10889 2.5 2.5 Mabsadd L .78571 .10889 2.5 -2.5 Mabsadd L .78571 .10889 -2.5 -2.5 Mabsadd L .78571 .10889 -2.5 2.5 Mabsadd L closepath F .83333 .01472 -2.5 2.5 Mabsadd m .83333 .01472 2.5 2.5 Mabsadd L .83333 .01472 2.5 -2.5 Mabsadd L .83333 .01472 -2.5 -2.5 Mabsadd L .83333 .01472 -2.5 2.5 Mabsadd L closepath F .88095 .10889 -2.5 2.5 Mabsadd m .88095 .10889 2.5 2.5 Mabsadd L .88095 .10889 2.5 -2.5 Mabsadd L .88095 .10889 -2.5 -2.5 Mabsadd L .88095 .10889 -2.5 2.5 Mabsadd L closepath F .92857 .01472 -2.5 2.5 Mabsadd m .92857 .01472 2.5 2.5 Mabsadd L .92857 .01472 2.5 -2.5 Mabsadd L .92857 .01472 -2.5 -2.5 Mabsadd L .92857 .01472 -2.5 2.5 Mabsadd L closepath F .97619 .10889 -2.5 2.5 Mabsadd m .97619 .10889 2.5 2.5 Mabsadd L .97619 .10889 2.5 -2.5 Mabsadd L .97619 .10889 -2.5 -2.5 Mabsadd L .97619 .10889 -2.5 2.5 Mabsadd L closepath F 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "NumberedFigure", GeneratedCell->True, CellAutoOverwrite->True, ImageSize->{500, 200}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg003@3