Polygon Vortex Iteration Construction
2020-03-15 07:38
This example demonstrates the geometric iteration construction of a polygon vortex. By combining circle, intersection, and polygon commands with an IterationList, it generates a sequence of nested or rotated polygons forming a visually striking vortex pattern. It helps in understanding geometric transformations, iterative algorithms, and dynamic polygon generation, ideal for exploring fractal geom
In collections
Lumei Junior High Math Geometry Models
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="w" id="BA5CD81E-883E-4A05-A216-59653C87EEB8" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="2048" height="801" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.2353515625" orientation="1" />
<pane location="1" divider="0.6669921875" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1,3" size="1288" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="true" inframe="false" stylebar="true" location="1,1" size="262" window="100,100,700,550" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="482" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1287" height="747"/>
<coordSystem xZero="426.74180146506444" yZero="482.48226634109693" scale="46.72206635048832" yscale="46.72206635048833"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="239" b="213"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="多边形漩涡" author="" date="">
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="5"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.16"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-25" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<element type="numeric" label="n">
<value val="11.96"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="57" y="35"/>
<labelMode val="1"/>
<slider min="3" max="12" absoluteScreenLocation="true" width="200" x="79" y="23" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="true"/>
</element>
<command name="Point">
<input a0="c" a1="1 / n"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.325742465628343" y="-2.5075789361572704" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="c" a1="xAxis"/>
<output a0="B_1" a1="B"/>
</command>
<element type="point" label="B_1">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-5" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c" a1="2 / n"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="false"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.4848191515761457" y="-4.338856276020261" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="C" a1="D" a2="n"/>
<output a0="poly1" a1="f" a2="g" a3="h" a4="i" a5="j" a6="k" a7="l" a8="m" a9="p" a10="q" a11="r" a12="s" a13="E" a14="F" a15="G" a16="H" a17="I" a18="J" a19="K" a20="L" a21="M" a22="N"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0.51"/>
<layer val="0"/>
<labelOffset x="2" y="22"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.8312773398629902" y="1.8409233140521972" z="12.53789468078637"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0.6654710406700399" y="2.509925026319736" z="12.543779139463929"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.6786476864567454" y="2.5063943547222385" z="12.559855779546067"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-1.8409233140521963" y="1.8312773398629893" z="12.581816878305755"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-2.5099250263197357" y="0.6654710406700417" z="12.603777977065453"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-2.5063943547222393" y="-0.6786476864567454" z="12.6198546171476"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-1.8312773398629898" y="-1.8409233140521967" z="12.62573907582515"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="m">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.6654710406700417" y="-2.5099250263197357" z="12.61985461714759"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="p">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0.6786476864567454" y="-2.5063943547222393" z="12.603777977065465"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="q">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="1.8409233140521945" y="-1.8312773398629893" z="12.581816878305748"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r">
<show object="true" label="false"/>
<objColor r="102" g="0" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="2.509925026319738" y="-0.6654710406700417" z="12.559855779546076"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="s">
<show object="true" label="false"/>
<objColor r="32" g="32" b="32" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="2.5063943547222402" y="0.6786476864567454" z="12.543779139463941"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="E">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0.025105874743590384" y="-5.004327316690301" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="2.531500229465829" y="-4.325679630233555" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="G">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="4.362777569328818" y="-2.484756316181359" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="H">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="5.02824860999886" y="0.02516871013837685" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="I">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="4.3496009235421145" y="2.531563064860616" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="J">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="2.5086776094899177" y="4.362840404723606" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="K">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.0012474168298179932" y="5.028311445393648" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="L">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-2.5076417715520573" y="4.349663758936902" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="M">
<show object="true" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-4.338919111415047" y="2.5087404448847077" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="N">
<show object="true" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-5.004390152085088" y="-0.0011845814350301964" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="a">
<value val="1"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<bgColor r="255" g="0" b="0" alpha="165"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="53" y="89" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="0.75" type="0" playing="true"/>
</element>
<command name="IterationList">
<input a0="Polygon[Translate[Vertex[S, 1], Vector[(a * Vector[Vertex[S, 1], Vertex[S, 2]])]], Translate[Vertex[S, 2], Vector[(a * Vector[Vertex[S, 2], Vertex[S, 3]])]], n]" a1="S" a2="{poly1}" a3="10"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.02"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<expression label="text1" exp=""多边形漩涡""/>
<element type="text" label="text1">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="127" g="0" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="2" size="16" style="1"/>
<startPoint x="-2.042000000000002" y="8.688000000000004" z="1"/>
</element>
<expression label="text2" exp=""多边形旋涡""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2" size="16" style="1"/>
<startPoint x="0.7118306430509098" y="8.186330276402667" z="1"/>
</element>
</construction>
</geogebra>