REMOVE OUTPUT BEFORE SUBMITTING

HOMEWORK AND PROJECTS

We will study a now ITERATED FUNCTIONS SYSTEMS (IFS)

Affine transformations on the Euclidean Plane - REVIEW

A transformation f:NiMqJClJIlJHNiIiIiMiIiI= ->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of the form

f(x,y)=(ax+by+e, cx +dy +f)

where a,b ,c d , e and f are real numbers is called a (two dimensional) affine transformation.

We will encode the data of a an affine transformation in the plane as a list of six numbers

[a,b,c,d,e,f]

EXERCISE 2: Define a procedure that takes as input the coordinates of a point and the six parameters of an affine transformation and produces as output the image of the point by the affine transformation.

transformPoint:= proc(point , tr) return [ tr[1]*point[1]+ tr[2]*point[2]+tr[5] , tr[3]*point[1]+ tr[4]*point[2]+tr[6] ] end proc:

EXERCISE: 4 Define a procedure that takes as input the coordinates of a polygon and the six parameters of an affine transformation and produces as output the image of the polygon by the affine transformation.

t:=[2,0,0,2,0,1]:

transformPolygon:=proc(poly, tr) return [seq( transformPoint(poly[i], tr), i=1..nops(poly))]; end proc:

with(plots):

transformed_triangle:=transformPolygon([[1,1],[1,0],[0,1]],t);

?color

polygonplot([[[1,1],[1,0],[0,1]],t5],color=COLOR(HUE, 0.5) ,scaling = constrained);

A similarity is a transforation of the form

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2MFEnJnBsdXM7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EwbWVkaXVtbWF0aHNwYWNlRicvJSdyc3BhY2VHRkYvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5Ric=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

A similarity with |r|<1 is a contraction.

EXERSCISE: Write a procedure that gets as input an angle a, a scaling factor r and a vector (e,f) and gives an output

the six coordinates of

the similarity obtained by first rotationg the given angle, then scaling by r and finally, translates by (e,f).

(The similirity should be expressed in our usual way. Note that changing the order of the transformations, it does not necessarily give ther required similarity.

newCoord:=proc(a, r, e, f) return [r*cos(a), -r*sin(a), r*sin(a), r*cos(a), e,f ]; end proc:

EXERCISE: Find the coordinates of a transformation that sends the square with vertices [[0,0],[0,1],[1,1],[1,0]] to

a. The square with vertices [[0,0],[0,1/2],[1/2,1/2],[1/2,0]]

b. The square with vertices [[1/2,0],[1/2,1/2],[1,1/2],[1,0]]

c. The square with vertices [[1/4,1/2],[1/4,1],[3/4,1],[3/4,1/2]]

square:= [[0,0],[0,1],[1,1],[1,0]]: squarea:=[[0,0],[0,1/2],[1/2,1/2],[1/2,0]]:

polygonplot([squarea,square],color=green,scaling=constrained);

ta:= newCoord(0, 1/2, 0,0);

applyTransformation_a_to_square:=transformPolygon(square,ta); polygonplot([applyTransformation_a_to_square,square],color=green,scaling=constrained);

square:= [[0,0],[0,1],[1,1],[1,0]]: squareb:= [[1/2,0],[1/2,1/2],[1,1/2],[1,0]]:

polygonplot([squareb,square],color=green,scaling=constrained);

tb:=newCoord( 0, 1/2,1/2 , 0);

applyTransformation_b_to_square:=transformPolygon(square,tb);

polygonplot([applyTransformation_b_to_square,square],color=green,scaling=constrained);

polygonplot([[[1/4,1/2],[1/4,1],[3/4,1],[3/4,1/2]],square],color=green,scaling=constrained);

tc:=newCoord( 0, 1/2, 0.25, 0.5); applyTransformation_c_to_square:=transformPolygon(square,tc);

polygonplot([applyTransformation_c_to_square,square],color=green,scaling=constrained);

polygonplot([applyTransformation_c_to_square,applyTransformation_b_to_square, applyTransformation_a_to_square], color =blue);

EXERCISE: Design a procedure that takes as parameters one polygon and a list of transformations, and gives as output, the list of polygons obtained by applying succesively each of the transformations of the list to the input polygon.

Test your procedure with the list of transformations of the previous exercise.

applyListToPoly:=proc(poly, listTr) return seq( transformPolygon( poly ,listTr[i] ) , i =1..nops(listTr) ) end proc:

listPoly:=applyListToPoly(square, t);

polygonplot([listPoly], color =yellow, scaling = constrained);

IMPORTANT EXERCISE: Design a procedure that takes as parameters a list of polygons and a list of transformations, and gives as output, the list of polygons obtained by applying succesively each of the transformations of the each of the polygons of the input list.

1.Test your procedure with the list of transformations of the previous exercise.

2,Get a list of 3 squares. Apply your procedure again

to this 3 squares, an the list of 3 transformations. Plot the resuls.

3, Apply the procedure again to the list of 9 squares you got in 2.

.... keep going

listTrlistPol:=proc(listPol, listTr) return seq( applyListToPoly(listPol[i], listTr), i = 1..nops(listPol)); end proc:

ourList:=[listPoly]:

newListPol:=listTrlistPol(ourList, t):

polygonplot([newListPol], color= green);

l3:=listTrlistPol([newListPol], t):

polygonplot([l3],color=magenta);

l4:=listTrlistPol([l3], t):

polygonplot([l4],color=magenta);

l5:=listTrlistPol([l4], t):

polygonplot([l5],color=magenta);

l6:=listTrlistPol([l5], t):

polygonplot([l6],color=magenta);

l7:=listTrlistPol([l6], t):

polygonplot([l7],color=magenta);

l8:=listTrlistPol([l7], t):

polygonplot([l8],color=magenta);

CANTOR SET SLIDES

SUPER IMPORTANT EXERCISE: Design a procedure that takes as parameters a polygon, a list of transformations, and a positive integer n and performs the following algorithm, with n steps.

Step 0. It applies the list of transformations to the polyogons and stores the resutl in a variable called temp.

Suppose that you performed step 0, step 1, .. until step i-1. Then

Step i. It applies the list of transformations to the each of the polyongs stored in temp, and stores this new list in temp.

The return should be the final list of polygons stores in temp.

Apply the procedure to the lists of transformations we found in the previous exercises. (and the lists we will be finding in the following exercises.)

EXERCISE:

1.Find the parameters of two affine transformations that map the large red triangle in each of the smaller, green triangles

2. Apply the above procedure taking the red triangle as the initial polygon, and the two transformations you found as the

list of transformations.

yIpyIr<K_Tn^T^;F:@Z;B:yypH^BnZ@vZ@fZBvZAvZCF[BN[F^\\G^[EV[FF]LV\\I^\\WN]Yn]WN]V^]Z^^hv^ZN^fV^V^]bv`c^_jF`n^`nv]aFaw>al^ahV`nN`yYU@j>`j>lj?lJFpj@\\KS@LH@LSDMSD=:::::::vy:U>KR:wU:wu:=bBDjB@j;@k:xY\\w=@j<@j:@j:B:<J:Z;NZ=^Z?nZA>[CN[Evy>Ug[J;@j;HJ;Lj;Pj<LJ<R:uU:?r:;B;]R;_RB]SJGr>]TRIbB]E?_SZ]VbKrB?Tf=X?_Tn[ICacR_eZMb<gr?kR@oRCGsCKSDOCGecGiCHmcHADKEdKIDLMdLaDOedOiDPmdPAESEeSIETMeTaEWeeWiEXmeXAF[Ef[IF\\Mf\\_v^cV_gv_kV`ofbAGcEgcIGdMgd_wfcWggwgkWhogjAHkEhkIHlMhl_xncXogxokXpoXr?yrCYsGysKYtOYv_yvcYwgywkYxoyyCpI@Z=F:=R:Z:J:R:?J<:ZoH<?R:?B;Cr:Cr;EB;Cj:DjuFZ<VZK^Z?F^knZLFbKwZ[GhMN^lFjB^\\<Gl[Hp;I[]V`L?xONflGtDn\\^^`[i^ky\\RF=GsCK[on`q::::::Dr;Mr<;::::::Je[\\Yv^=NxmaX:oP@Hj:NZKVZK>ZyrwoID?GZOBD??:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZefsxY^dQ]nOii>kgankytSq_HxmjN]Awm`w`MF[<igb_sypaAGxaovZqkeNtbbbOFDDD:::JSmy[DxHxm[eM`dSAItJ\\OdqXAMmF`QHYX>HrWmkI<p:LL:aJHXn;uQOprmTophMhDRiev_`rrPPLLNpYXLula@YwYm:xRFHOTMM_LtkPLEPympNXpKwLuLeoBtpRpWuuyYujMQtbQnDXPR@o\\L[KgB::::::::=RksYJyfQyD<ke^kCGuXGcyy;BuQHZIUY=doudiMDqsUfMR@sBrYusAR^wvHOtvyE\\yQfyWfuuKHyYAxKhyuTYx\\WsyMTuq^iu^imsHuuiKwtpaiveYQwLY??_\\PKK;::jOxL\\umJHWxIMLaVNeXSPk@uNfIxZXsFuVr\\rW@uZUiL>C[FXIFkosYGFWmVGubK?TfMwpsBT_svmcm]r;gEHwCj?RLDKYTqryK>QyAPKoXVbLWFtLbUOiqwG`LqXRvYOdms@pV@Au;<T?hta]R\\UN@mqaIpM`VoUxThqZtpygbaIyA>kvybb@iepdtnjZHrpOjppxbIuE_hyNrx`nZqgfgfBh]:fdVojOghdNsS>eZOjl>[_PnvHaHYdQ``XxndAevg`ffa_nbL`pKWwYp[xW^nfs@Fji`uPfmBpkHqx@GsN`xK>sIGxpqdyVi[HyjxeOYw^qpOgH:xth\\ys@yFTTnLm@tQjMUpMNuXQSUM`XTJuR[xqAEuRiyhyj`ERyUtCXkauxaHQj]y;YRyyTxtnFhqHYoqPmlaYwpPoMybPNwXJ^QRD@OZPJD::::::JsdQPUmUtWOlu;uoRpRYHW`dRqMw`YLEAUV`Q\\HwKLpj@W\\xKXYjRxXFhLXuxoelXQw<qsuASuiV^tLX`Re\\Qx\\x[aYsxlhQqaUnF\\mK@SZ`KwpNmuTxhjkhqr`pLtvTqyFmKSio^\\RGhoA]LCXRJLjL\\unARImseXmjasTApkqLvlwnYu[=oEeNTQSGuYnDsS<LCMXO\\T?aNx\\Ta=QJUJJHLEhvHxVi]jJho=]UfHtCdUOlm:UNmQOL\\tM`dm@\\ungx^pBF^U;:::@j[]Ycix\\qNjyOBpT]qrKYn:HWQLnAukPiLSyTDawJpNRMjkUU]pq\\XqDUxy=jBxY:@uYAUxXnmyQ[YNuyXpayRMxy\\pxIsuDSuXxmtXULyhysEuTqQynM[KK:::ZPweB`i=wnryfCWlK_t^W_Tfmkpr=x_m^m[A\\qWf=`WCC^=BB]y=KFWyI:SRt_cToC]EvRadgkCnEesaEa?c=SIVuEZCb^LLxpXkymBdXIdldurJ]TRpOJqtXeUUDohyJrytN]mGhsFDp=<nDXoIAK>qRF`YIUvaHsdmVoTY;qWyiraEyA@KvyRb@YelttpjZDrpQjppxbEUE]xyPrx`NZmWfiVBd]dHqnFdX_]aI_EQmUwmcHfjaxj`tOP_DGt;gBct`EvBOcheVSSBe[SJmB;_Tn;d`wG]eymIvI]b`GuZ;toWy<WDkItSquBCeloE<CyCkyxQsAuGnsIpYcteivqdDoW_BFrOWGymCxSvncc@Gri[ePgeBqsHmx@GsN[xK=sIIXpkTyWy[GYjyuPMr\\IywIShmyu[BVyqdyx>IvQHQOqXmmuYyl`pUidRNxTZ`YBDT?]<O>::::::VZE@y=pZvpuJFx^>ldOedGgyUpiF;;hxqEgqGYaFhmeZ;eFmUjmhkIt;sbwefsyAJx:Rx]?:n`n=FWJ:@?:bO:VL:HB><AMp=::Zd;TeJ=::JI::D?:m:ZG@=jd;::Z?:g>JfiVBjV;:<IcPO:c\\NFDL;HLOfL:_LZjtsI:hJa:::v?:BFrO:n:nh\\jfKb;::Zjkd;Biy?:BD;:::::::A:lE::dyw:::enyCwuiHUt?CxW_CXiRuiuJYD`UvQKxfqCLCVriIG?vQav:kyV_IvYR?MI?J:@?ZP;::HBjk^w:::bTjcTeJ=::JI::D?:m:ZG@=jd;:>D:P:nL:hVBjV;:<Ic@Jd:L;:rBfL:_LZjtsI:nCI<::v?:BFrOW?J=JujfKb;::Zjkd;Biy?:BD;:::::ltxHnf\\u=AOUdKqxSuiYNEpghSDIM>TU\\PV;qXL@PLEpAQUaPwvujmynEUq\\ApiaXWMSglVGUTBUW=iqO]qpYlgDugIPd`pFLlhHTP@nDEY<uTputHTmH=VG<kittKIt\\\\tnUpWLrVYuCdwvmrbmt:YSsLppQlZ\\VyEk]XToXTLexeYSgpRiisNaoZhpxpPDXO<hOh`sk]PlEMOlY`]ruTpM\\vgmrpLXl=rg`puesYXrEaNcMj@TyPpmPlxLhUBqSsElDxOTdL@yL>`ncHSE=XjTPYIRMuOMpsvXpPaPeiMq`mHQvfiuoTvjPU`iuJmRtd:WGqKc<OW;^y;WjXwgB>IKTGUSGcsylh<@fwgaTiexHCsSj[S@sCrSyrAsZWvXOdvyqH\\PGPk=URx<NEySA<txUwIamAAO;Ew^EkSPxClulLv;aPtmor=VXXPd]\\\\\\\\\\fxqJ>yAxcjqsMp^]@oBqdoVa]gk@neaGa<A^hyrA>UMDB?RJ?yA[RtwY@_HScXWmb<GxcSUV;wlSxskCKuBp;yx;R<CK^`ygMVyHLdmmdhtHHNb<pWAnghQtlpLeuI@xiDOrXMUDM\\uJ:elQumK@KG@msqM@ysMhTFQwpQjWqyExSlukK@YI@TkqTfdXGHr<dW?hwgItlpLbyY:dJwIs:auRUSJLq:POs\\PKmeHYDXuYDo[AxnApNeLdPSKER?GoqN[bNN\\<::Z@gdocl>f<lLGjofiSVwYp;ACGU`i<nx@KtkrUiyRbmqiPG:Zi<j@JpsW_?;g]xA]ohy:TuCX;HqsuWJ@xy=jOywCTRiXxdhw`aQytoGeqXMkbto:EyJPND<o:PND:::::Ir`syKcHGKIwyT>qXLAye_WQubI;EGYfIShUGs>Cfp]X`wEYYfrYXm=HAiDcit?]y;eDiQfjwBCcwMYbtaDJculEvxOULWeB;bj_EpMuJ;ySyv_sCAAbkqeL\\<;jELVyHlU=ytesSYlIiQYPnTeTUIwJ\\k^YlH]tVikGYjFNZ?adXX^ki]yxjfhtS`auIuli_ghdpHmBnrC_agibBauRAaBAZPN_a`s_nl\\qwlYgeIwvXySIx`IcG@n;^m\\^[W@os@aVom^PlRWpYV`k^s]_jGplmXiiftXp`gWm=WZH>eey`lhw`yYUGMYu>khtourUfKQUpWueaXV]sF]R>IR@kD^_fBqydSVW;hqMTxIh@SG@CES;E^=D@;c]KBB_I<sS>oXiWCfeSuCRqgVi_GNWCjuIsmEjsv=[HFur=wu[SV?mihkRtWdOSwuwuiiHwuoo=XImMIEjMMwsaKiLSIEsoUkyoxYYs`xjcfb\\>p[GlKPj;_ZZOjr>^=@sZ>xAOgT_xIwu]?_HQ_KwhF?_\\PkDN[bNNOBD:::ZmxncQheY`wPqvopearlAlB>dAgU[IPAvn;w;ICfEuncUpeyTaF?CtkOrAyxMYVhyhTIiZChYlKIAvWitg\\OPpTCeWgAMH\\NRdtYDm^dx^lMCaQLTxVAMVPt^Dq]EXxyuQixaEYqemk]rlAWEyO:YQPMyCuyaxlruQiXt]@xQUk_@TVHuduTMys_HQsqWheNcqmOykv]XpaNnxvuarLxjiHsxyOMYo?UoiQRxAoy?[hisy>dMpy^vupG_RxYIx]qyCwI`qyyhvYXyYPwuQpfXuT\\teeQtyqKymS`vStvw@pryLixrYIssIyoixYYtbPnDLymTw<LkbB?]<:::JIxpryKbHwKAWxXnpXLAuu^MQt`Y:EWXhyR\\UFunChP]PpvEyYhrYXM<@Qi@ShxO\\aktQXrYr>Il;qncyoatY`]U=XQdqklhWlqs]iVB@sBuV=tYr`mFHXT=T;@UxaNk]JxhMMQt[Mvm\\UIyNKdW:TqvEuDUpZmpH<TOHuCxV?<QF@X`dYeQum<tnUVsAYFErgEL?=M@HsVLJ<=N^`VVXLHGZ^R<wRPquXmudOYEKgtScc_Uc?S\\MRFqXb;CuStrmCjSCk?BkWB:OrdIiSkBx=UDyI:mEuywOCYXmdeME=UbEayXYSomiYCeNQXViUXeSwciquEukyvCck[PaAK=tNdmOHulaDo^llf`r\\PkrQKOdNLmSmuxfay`eoSitUDoKiujPNDLoF\\SGTY;up_uof]lE<PyDYX<XaXJn]KAXrYIN]eJsAO^IS\\DsJeVWTrcdx@dqlDQgUY;eVcyOfUng@qPpMWmJCiQWyjiPoqMWx`w@`XjAyiDYqypcmyY]vxYO:]meeXS`Ou@pYpwYTralXYyvwyTruqgHQdEoOhLNQPjdv[=l;=s\\pLwXnqaniMOD@o\\HJ?\\LKCD::RgGWtagtihCKS\\WF?yciyvAaeiexmEB\\sqVpm;eKqhSYpTsDP>]sjInwaxrYyWpXh<YfxRZIjC]wUPqohp<PSSiogTnK`R=Pk]Tx^pm^XLCyNLlseUlMDkNuLflyiXstqyvtyiXVXHQHTUS<VjPLwxVkYSsyQuywE]TgdwZQPpTSeAW>ExZPrb`YCyNc`NlIs^YlTPMDXO@iWqlXxEJcLSLQxMTQ[?_^X^qOrxg^gO[egi`>xQPt`IlZfphgod_w;Qdy>iEA\\A^h^v[spyiXtefr^nksNnrgn??iWQcl@`BAftOjuNkeaiaNvCi__yjAotavfAGfWfmfioLHcZiben]gHuVgyhi\\x`iSnai@_Fiy\\`devauWniiveIyYhgKxfXFtfn`[VyWy]yw_YwsQqitQkbvoZpa^@_\\Pk:>?O>::mWIgt@qruebQ=tekbkyVTGWKieTGu^QHPsFI?WT]ff[Ct?w=wx:kvwSV?wxWPQDYoQTyhYQyQkmhWUyny=j>xJuYlHYU^ukmdWXmrkiv]uwimYVhX]imdhQNpTtyY:<kZYK=Uo>pPqLuNuTmQOH]smYSxDNiaOLHvHDw;Xmq=Mg<NLqswUJ:@MyIl`AxbDTvqRQlu[LXoyiSYx;ffwYqfFey_^fyemHk<_mvyqhvuU`a=pmugieOem@tnWvs?iFIbgGl??]@FcVPj<?^^^fVX\\HA:_FJCb]adkifQOsU?BxEfUcSUoBHWR`_ECkUwMUQeFY`V?pP:YlHDuSdxOhMc<y]urTpPgpN[DyHpjiUX^<KoHm<DRKHqTYnBMWjUKqlTZ\\X;dtk]rH]nctPDaqL]wmQVdhT?pnbYRTduOPtuuW]QnpqXmyTNUuK]TSaS_MS?MLLXVqLr;AuSlrm=jS=k?<KV<JOltdTpatJvetPTpginopmGxVVYUGAXFdPSpx?hK]ltAtxSlS_]ukAunuwmmyJtQRxiYheIvYGrNyevuCYUFUiGFUwGmckUYxYwvwc?wWNovOKgtcT[qxvYVxmFOeTaasjwgDeXUwdrQRImRNWsCiWBeY@=TqcReabA;CIWeJIdgoCWAwN[yuOFgQGOkgaYhKCuXKVE;XMGdNiuLOCkIG`Ir@sv>UiauwDyCusuU_iYQCySxi[wVYRxiIxIHyOHogtesYBw=:jcxr[uUOXsf`UcUwaUnsqxpAXVUQWlrWeN^EWO@rwmrmAMU\\QqeMuymRAyYaVvytsyJpmk[uyxtyRxY:DmTQkOyY:\\jilrYXxeInyGrNxuvykN_xYp[rYoSGtfhhEWiwBRuwgWfres^]D_[sO[DjsBJGDVuUMyBpkyqCIyiTxIfwWRRyQYxY:\\ky=jFUvoew?hl^xqj`kpLVTUYnEm^tXnqmxXoYAosMpUdMPutJQs;iL@DRA@nDdxEuuH@ydpReqsqpLImRitYjiW\\YobXs:LRchNEqy]qnR=ukmmBQyFXsiaJXPosdqe=KMXRqLl_aNFtuDARxpyjiy:ErvxvNYx;mSw]OptkRtLg<svqwy`SwyU<@Y=xm:Pj:qVKpYC]ylLQhmqHispTQoUugypYDTWixQTRIdLYeUdqPkqPFpm<=vUMsTmWVmLktRhxTqeqp@s]\\MlykNQmqTRIFtnXggQd[ap`OjDquEGkPVasXcOfbf>bFA^aWZNydI_teyy:v_\\ykKyiPacipyxwYCifyqK@SKiuQ]yctYRxiXPmYny@fcyAZ@QgVxmF^aOo\\mhg_XpbouwgrvxtBNrhie[Xfbgt;hyHYhSxdVnhwVaYXdi`yyPkIfxMX_yAZYxqsa_y@s^AghXwxa\\yAZFxaaqnAxy:FjMxikQmapnv?`kqdePgqA\\p^kbxlMVuJxxlWjtH_To^vNbr_u>xkf_hcybNYwyuEHrxMP_yY:Xxquy_xLsaMGhLQMWy][ePcoXcCXu@_fu[EGqCgufVoLnm[_]h?hIopt_xexmjynvIfyUIcsIsI=qvylrbQYWxY:hVv=tyGelvqsYyyAZLXsvqkPNkeYnrIf\\IooWmWh_UobmiW\\eqNhgY_]>cdxZhYhV`RAIhQipIIyMsy;B@yumUt=yq;Tly=jkMmxtnYEYy]lYTW`:CqyS[QgPWu`pD\\CqA^ej=RKEGyYSvgTg?GpOiW_HT]YjqE;iE<wbu;dtWVb]gyCGZkhI;yAoDtqdjwuB]h=ivcItcKidiwVeGg=SGmBLSrB_fNkD`aClUVhCi^GdXaVPgdj?E_yuWQrietc?IYiG?]YQee[gYH_cssvggFqQwloVmwWqiRdodogx<QCSgggSvK_B=Os]Sh^oe^YDCwnV`tOYOy=kY]kyxVQYryWjcvqsq]cHurwh?ydQQeG`qPOijViEFjiG_gobVo\\kvbhvdqi]p>s]`mlw[NIyI?_Ay`qw[?yiS@yfOpvNsLOhNp_YyxQHyO@oePaqxjvgd]@gQQu_hrX`kJIeUGskO^AAoDAedH_\\oZZWZrn]\\poyOrQVvIFyoAtyEvEuGyI:AcnwykGxy;rC?yiSxQkXHIFyqIyAeyGUOebSYd=dDh>>qqPm[MSV;ldh=FWbY>ZYhEyQ=bvxKfwUJu[xB:kryflGOlrnvCPvOh\\]ihd>s=I^;PwBnwdnuSHvYi\\dopiHh?nMKw_aZtakZpwDpdCxkJn]qF^]VuWNaKGoryh?QeOOoVwcaWnlfa>q\\Zq^]H_ufnOPfM_s=fkHI[pysX_lyWf]yiMHxYovEF^FydvYqvYFIUK=yIgRLYEEocI]wHosHKBuYYSSe^Yd:MCPeiUOxsYIVUwv;YlyxOcVL;yYgRMaRkUc_?VvoW_CUU?dNkbA;w]agvQsT;ti]YgUVkGXZeuRCwQYxSSrNUGkoGe;Wx_S@eR?qFuCyhAr>EI\\CbZmGqqH`uiKyDEitCGcCgsTUgowggquaIU_Yx@SYywfFgrTIEWYytIuiIYxiIgcDVmb`whCkg]kssKC=Mv@iVOSeVAB>MR@YYZyVJ_tO;gX=VKcBN=JD:ZOowf`_iaqIppTGbk_vDWp=yv@w]EIlxWwhPijFs;a]DHp??Z@?^?pgXFv\\_kH?wbPx?V]S`dL@nX`n<^s:gwrPyNqhpp\\poay?ugA^qXx_Ig`Qx]G[`AcYIiUi]R?v^omG?efxqLNwM?gXi\\OixEghGxnlPpTPvo>lLfnKX;[UJGxKKGbABkoGUoxmEVWueEuxbmtuSeciW]CGCKsS?Dbsf:]u^KyT_ThqGGqvK]YOGg_iwgiEVyTPsTQSto_U`kRMabjqw__g;aBA?GZAfTUIOmygiR\\gSf?yduWEYgUUIB]gfighEVeESF]g`iT`iuGIe<=C@GT;Wbssxe_Yu;BpaVMGVQGupcdSavmiwgoVqcR>cGeUv@]CIIUHMVVYxViXgOxl[ioEgGaWrutBcDhkdoqupKcUCCP=h<mBn]s:CCaCexoFo;g<oeSqf=efTgIvcC]YVVuSjWSJqSceVc=EjsbU_u;ggHeybatn=UoUeNwhW]VNWCBkW;Kr;ceNSgdms;UFl=bwYhMegVOF:OCaoEU]sTicH?GgwVYEPUtXLqrJIpn`K^HxVlvPuswtjHuxexMPYSYAYAhsJmusIvm@qnHqt@MUasJAS`yN?dtver[dLy]yCMU;eNNuvheVZqk<PPvip`hS]<YQAsLmWTppXPSDUMsMMlPSP\\RD@SBuJSpm<XnjiroirxMk^QqMhSTXmuTOMENJaK<Hm^EkSAj:]U<MJjAJC=Q:<xm\\XEErA<K_MqOisnMQNEPCiKMiuXeslMpVujGMN]TokDy:dLYmw@lvETXl<P:ikEeUpXmeeotLvP=lwhj;AQBD_Rgr^>ehOagGlI@]^y[[HqVwe=`oh^`UWkgw`TWipptTXsq_moWiU@shflD^_Hp\\L_ZhG]JHln@fBo`kHy<pxNHZHWsGoj@YwK?qC`nivijo__^[@WZBVnEX[AickHoaaaM`x@fo`Xrf@wQQuWWrB?pXWuCyg]nb:?fhhnCG]>vfA>tOQsb>ZdPhc?pEaoUQgFPtsoxpYxUOn<p`OHl]pfa^kaI`hFahQipIq??ZOvlZHgmHgT_hpXxn`giYiq?hDN\\@Guh_^OxbZVho@rxFyeqtsxqqpuwWlxQ\\ifpIqxYhwy`wYYpsyjfyYIuxiUpgUxuuGAuwqfywiyasfCYeYf?MeXwVdQERovTyI:MwhaiU?cy]h`QhmYfl]fWmIf?vjWBlkhkWbp;BocHwkXWqDOiWaCGOQD\\WS:?T:uH?QgDWVJAiV;RYawnUGQSwiYrLMeGMV<_wxkT\\wBLmhUIYXEWLeRpCeKgeSSSOAhEiU>IhlKTkOENEBHcIp?eoWUWETTssxQFXUUqMt@?dk_hF]fkaU`qDIgYAqCq?g\\XTLaXR]XgQMAYSqDWTTKe@ygUVc=KfdTN<Oa<jF<VtMKi`XRywh`peEKTARpul@LvZ\\nZIPD@sj\\unUU]lmk<SYTrlIPvuSwEx[QNCdo^Qx`PmhqTN=SNTlRLmrMV`=Tlup:`vFLJllJ;]MJhkDXsLapS]OoemlMvPak_hyd]U>alVdjP@x?qj]qobAukmmBLYDLYkTYY@\\n`@mEeUYuUce=wGaCG_XBefsgtQ]S\\GuQshZic>=dSmrpewOyCkoIIicxEXeeViGydEbyAWiCg_yXOmW\\UErUFJmeNeC^IthUc>=r]ugC_ieeRZ;RteSUgSAIeKwgnWi@EdZgiqQTXobFAR;eeDKDlACHwc[WwOiRW=UV=erQX]adOqugahEYSUghnqTYwTsCD=QH?Ku]SUcAED_xZKXEaFBsxhiU?UID?BaoFU_stgcpAGGwVYuGigHt;W]EGSKUpMvrmCmQd]qeauge]TK;rNaHGkHWQwOiWZCGSqU\\WY<_U<uHEUwDWB:AyV[VI]woUg@wv`WrdOe_aIgOV\\]U;;HD;tH?W_EUNKHIWEJYbgoUWQG_[T:mDVMufEdrUwJcdSYFlkgfgwgED;WY=qbmSxMkbkECQaEpcyuyvrcR`SCwqIhYeU;IFOiWQTsAXDEt^uEoKsWAi_qRPiXTqcM_ILCSDobAECoGWnswDQgtgvtqrMEUSeCkQEBEsL?c?;BrAF]YVN;d@cvOicSaFTwiDcgnghwWiuQrtQs\\Mg`WyNAS<?GXidVgIJ?xRcFN[RUuddyfGWi^;f<Kcb;>::Zl^wvia`HgpyxJOe;_^cNhXXeNpm:?s:TdqbUSHTqw`OUb[T`qCJUXLMGtofWaWsueiyXm_ifGRAafVgwGGtpKtqqBRWeKOhgGRJ;XeOBDDT??:bdoe_iVTQwPSwGMUBKRrAIXEGXCW][gK]DnGvN?VJ;C]GvB=gBWWN;T?=YfiggqIHiw]Mh]wxBSBNCXkACOmIXkhIwdG;FH;ISSb:auaAGXAUM[hGUBHyHCME>EVBqFNkg`cSJSV;MTAeVV;f;Ir:WV_]WK;rSMi`Uc_]fsqVOuFciV:GYhmg^?iKABHudvacG]h_=sV;VPKV@IcHcRN;T;cRNZSvy:>uTxhpyrpyoSyy:NttqwXYuqfgSqvfoSasSMxiqbgsYhqXkib`eSeeI`eg_qTsSfLahSqRx?YYCh^GDw[upwuREfm]Hj;B:]SbED:ID;[bpqXkYuUcBV=h>Cb]kCoOcb=FZlK:XJF`TNDT:e:nkrG^txpPpu\\A_`QjNG_^NhbffoW^>>\\r?^HH`LGd:G]pQigflGHmpxpSgtTgdS`veGmTFeV>\\;GiEv\\xg\\QovaN_<fyXQ_<AeUyrbhsxGp\\QwbWn@xbVqi^Ob_qbt>h^wiIAuOOkbVZyVyP>sey]TqkmHsnGa;g_FykVvfhguCI]\\?kUQhqN_=pjhoi]gmD>_ZPZD@_Z<SRiQujoiYwG^GWbgif[FhcEPYcS;fUSBeMbvuxW[blCw>sV>]f\\mWUEU?WwqUssSEK[v]gsWaVsSDrsIkEYhmsUsGqCEaSBP?GZaCwUx>WTnswq[wPmiQWU:QxfUYOWHpiXVqsBsTaKGheTl`kT@t\\LK:@o\\L;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::j:xyf;:1:\"\{\}

EXERCISE: 1. Find the parameters of three affine transformations that map the large red triangle in each of the smaller, green triangles

2. Apply the above procedure taking the red triangle as the initial polygon, and the two transformations you found as the

list of transformations.

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

EXERCISE: 1. Find the parameters of four affine tranformations that map the large red triangle in each of the smaller, green triangles

2. Apply the above procedure taking the red triangle as the initial polygon, and the two transformations you found as the

list of transformations.

yIpyIr<K_Tn^T^;F:@Z;B:yypH^BnZ@vZ@fZBvZAvZCF[BN[F^\\G^[EV[FF]LV\\I^\\WN]Yn]WN]V^]Z^^hv^ZN^fV^V^]bv`c^_jF`n^`nv]aFaw>al^ahV`nN`yYU@j>`j>lj?lJFpj@\\KS@LH@LSDMSD=:::::::vy:U>KR:WV:Wv:=bBDjB@j;@k:xY\\w=@j<@j:@j:B:<J:Z;NZ=^Z?nZA>[CN[Evy>Ug[J;@j;HJ;Lj;Pj<LJ<R:uU:?r:;B;]R;_RB]SJGr>]TRIbB]E?_SZ]VbKrB?Tf=X?_Tn[ICacR_eZMb<gr?kR@oRCGsCKSDOCGecGiCHmcHADKEdKIDLMdLaDOedOiDPmdPAESEeSIETMeTaEWeeWiEXmeXAF[Ef[IF\\Mf\\_v^cV_gv_kV`ofbAGcEgcIGdMgd_wfcWggwgkWhogjAHkEhkIHlMhl_xncXogxokXpoXr?yrCYsGysKYtOYv_yvcYwgywkYxoyyCpI@Z=F:=R:Z:J:R:?J<:ZoH<?R:?B;Cr:Cr;EB;Cj:DjuFZ<VZK^Z?F^knZLFbKwZ[GhMN^lFjB^\\<Gl[Hp;I[]V`L?xONflGtDn\\^^`[i^ky\\RF=GsCK[on`q::::::Dr;Mr<;::::::Je[\\Yv^=NxmaX:oP@Hj:NZKVZK>ZyrwoID?GZOBD??::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::WgMuuOCHnQihERiUi]qvSMuWoEvOhoiWm[emEBgWI?GVZ[sG;SHIrIKC@=HG=bo]TKcjbPND::::BQgwf]y;AhxiB\\;SnYiUkDMkyvEINSbOmW@yTGagvIyB;GHCrFUeNURWcs^YdREiM]ULMXPuCiui:OFDGGJ]TKRK::::::::vdUxopy`vi^Xx\\xqsyE[YfmwInivIoxYohIwtq_GQcuxYTlqGHMyvAUIagQ]FQwTbwSiYS\\scDogcqfcqXJuyc=sOeGowbWUcwqcaOBgKK]aqaAp]m]p_lKgBcRNE<:::ersyG>wYBYw[eHwUfBETY=Eome^;eFmXdmB;AVj[vZevN;H;aSVeGQky[]Y=seIYGcMe>QstWrbSx^=b_UHLKHCwB=CFAOga@lGqROuYHhnSHmWIuWAuuXQklV`un_DkvLLCanMDs`<QkAUixVhUryGloI]HNbkikQooghcy_vYAxuvqLPxCnf`whpwhpo_hawSGmCHs\\wc^NlC_^lIcihbryhkY\\uy[DItoFqyPvOOrUgesvYYvMCtRyQXpuA<YthyIIQa]tQUmDaQcXSStmk=m_]lk\\pw`kOiOmdUw`qvxkf@WiHLryXkYLuykDEtoHqyLvOMRUeusxiXnmBxrxIitw]ZIwqqaaypQGqD_odwrTx^_Aifi[fg[aoblxt]@wQahNFd??gkgjNFd:gZNFD::::::JHtqQExHDpfmm\\\\tfpU?]OnaksqTMYuuDsoqPWungMPC\\lAELZHRN\\yKXqVdWWhrwixxHMa`uYmuCivTQu>UxFUyCQUDDk]IjC=rAdnlQyyxjoXkNDxPtm`mLiXvixvHIqTHVLUsWqTcUjg]k@MRFAk=aKt`vW\\Q]IxRqTnDwoUYmtvo`UpIL?uxO\\rLIUtXpyllOutjMLpXKClJjYpWXKHEKTAjIATvaUL<YPemYaRlAubUlwhu?YP?ipDMo@IXGMnBxxMlJfyRCeMj=c\\IqoYm<QprWp<Yv=GxInxGxtpaj_HnxiuPxxdgiLXvgFp_Afs>rWqkrysontrWd?WqJahShoiv_^iqKxwhog>nkMfjLxfjoaNGdLX]kWviY`;NxZa[wObwOiYO\\rgdogcqfcpXjuqc<woe?ov^wU_wq_aO>gJGZFXxXXrH@IUID?g\\\\LKeB::rDYhY=CyAtQYrdMi@Cd\\oyjKwvCCjEuf_dFMr;AVBIbDIGZKbSAiTmWvYbroBxuuQKdnCsOgXAIT`Gs:Uc`]F^KDImB<mSOsk[XmGPOx]MEUpmXqmXQktXqQvF]SHUSLDy^LLCyNLdsjQVkpuIau@xY:HLoEMHPrkekQqOgdsyGsy@vqwi_^vL^sFqwfqwfieWAumX`MNl>qmC_^LHc^Yl?_\\QokWixaGwKNkDHdDPp;gbN>djvo??YH;:DFxIVFl]I:ReKeoeVDaEKayvScgWfIYffQwiIToysteEooimOVvyr[yU>yCfsYearPqfyECQESgaxakIwciKysvQHnyI:IrMmwwuchugpetRgDI]xIOsk;uT;uToSGgViybKqGb?g\\QsJSFD?g\\\\<::::::ZefsPygDFs\\ysEfkI^ryNuqveTQ\\PxjuqhUgucpxE_kpxrO@jaYZpWa]aaQanQw\\bxciXc\\ycDnocpncqpJyic?sOgwowZWXkwokaQjgP[:F`XXhRIhIUAEG?]l<::Zsww>yaBXg[UYACL]vQkTWwBSkF=ggTGTJ;CvCEBEIO[Y:SBqUuOwSBsAQ?Z^:::xu=EK`mFWqh::BQkCeitfiYByGsueKAD^swRettQwNyTxiCyWruCIi?VPmVauXaux\\qwhgbS?eVkt^MHC_NXDSnDT?AyguUPqYK@mbdnRTO^\\LKeR=LkbPN:L;PKnyUAtYKxqj`YgTlUYMxeNVinoXtY@yn]X@yqmYsJuYAxsstxvPwDpTGDwLuLntSyPPEAw]AWuQou\\XwYtxuPWysf@Wi>X::ZXnMZZ=ioWeNPep]w>kDuUj@:^H>GZN::::::ZsOqdQ]owuE`aif]Ypkyxp^P]>`nTIypygjhiLXvaarkVok?r^Yv`IwVxd^xD:Zp<::@=:JD::muu:ZRKlbg::bIjA::NDj=:vQZhUQ::CarjSG>pA:FYJX;::BIr`CS^AX@mUQ]t;gtR;vDKXoaGwcubKRpKu_sH^OIDiWPYiWui\\_hrCiIgEI]uaUSfih>srCAuqKwkwtDOtqAhXEhmahBqXpAwSGsKaICyddYclaEuui=uedICHAtrMuYutgsC=yU?CIpQbdkI\\uHWYT`eItYGpUHdEiaKC?ccnCgTWT:gmm@YQetgAVe=VmdYqiQEYvNhKF<OILvphMWeqRqKv`x@ioxHM_DwDtxJPUUUufaKCxNTUJgamLlSseQlDswLpemlRMWEAsWuyYut=Mvkmye<vcuPVdLS\\twyuttqQ=y]xsGPSCHvIHSstOrlnJpPLuMnHJLTtETXFXxKlMcPT`EM_@WPhRmutuTNapkr@v<dQ;qm@hnthMoYsCtW^Lp@YXjHPp=YNiY:QQgIV=UYkLveXpMivoDxXdkEtuTYuHAwRMMcTnFDod<XBuJrtJsHMaUWIPuXeP_MSdlsx>unYhHh_GQhFoaYv\\FHnSnb\\htevnAfqU`iQYtCQgSprKgeFouHVtUx]aompYuuYu`VxqviYArRaykvtVHxSWprWdOWkXfcGilHQiiqd=xg_yqynnkvuv^bk^h__pgXwwYeka`:AySHl\\aheH_MwiXydWOi@yy:Vtl>_axc?fvXpiQIfo?ZE>qkxktO_tylGOsAne^XfiPc@H_\\imEWbd>cZ@vN@f@wiD>wTWogxkoPr`?ev^gs?pOYfo^vMayCX_KqiW^y>oy=QxnhchwgriljolQqcyWvMItRvy:vsiVbvi]xvvVYxdX_Tg`_PcVGt]N`EAg]AwuQ_u`xwWdxypWwcf@wiH\\ryhkY<dFxEh?:<JX:HqgithQTePmkpvCDYPUQ=TU=HuKaoo@WtiPWeJNDTT]M[eRN<T;dRN:::::VxwIiaPlEqrtyqUyg]XqKy@AVlsg_ksrmxScrloWC;e^wUvkXaOYpIr;OKQIWcHwEIoUiovtLq@x?]qmTkSMuP<\\[Ychh]@?hxOd^hw:NlC^Z<fVogt:nky<dgpmxrsZ^=gdsQVYiuSGgqUXSIUdQe@aeQAYMmHV_FLghy_d>wIS_YDceFMFVQd>=dNmWMGwdOi@UWsiY\\ssDerkIVwUSIGrcAS<WEciWSICuiuIKcvEyVwvVaHAwbXCu:cgbOFD;bbOFDZiharyjkMY^Nh<:K\\X^[>LI=:vv>yaB<Jf:g?:^;UuO[irmT`pgW=:ZewjONkpqi^y`vykb@slw\\FPgwhhdWgyeCyq:qWxYsCuLMDYKeSmUOCEn;hnKHMEXQXHUCxNLHSCaNXHs`apZAxpUpmMjgIVohUUySY<OhxQTQKS\\JumwStrhiPU\\Nc]PIYlFXNcltX@NQixZpuxHn[PUVQs?qNTYvO<K=`XBPSk^wSGcXfu?`ixq_nHw;QcwNyyAZXWnkYZw^slQcnff:PgjflMqhGongXgYgb_py]q_UIrKyvqvxLysIQyrxdCQbuvf>nqm?w=ypWVhgxf[HgpO\\^nppA`fHsWXplvwQxmpYuf>irVwMqkOHn?Gim^rOym?y_MAxAGvR`ymQ`Fi]kih_ya`^xuqpeAubNnD@rlQjsxcPNgEV`?in>Ir<@pPxvYVrF`\\=owHW]=@lN^f[gjnOe?`xtfgFxlmowb>mRFdL`rJdACI^msrwVVwdXoRPmbskGRix>]c^_T<ASVSyFWx;=da;V:oXiSR;qrlohIqfXyI:;xy;rBcyQWBXquxQDFoYsEuxogGweMut?QxW_iuUCQ]XgEbneYWofOQRUoSxaTfKI`MxKICn_RJKiIsu^EfdcE]OgteD__Cf=H;@KilSKQtE`KpxvhIYHeTAip:aT;qTTUwxusnmyFaXtToITrTHmv@PuanHuSqAW[hUU`Nt`M>LxuMlNxVVmmk`KhyT;ptUtNqxjJmyHurZUOZExmPRQqTNhmYhxaQQlQK_XY^HwTUkiYqlLJcqPfQLlhKdyQSqw]DO]xjDTQ?]S_AouhrRyV?HsMuLnhmYHLHysZUwmTLceXo]wpAx?`YNiOdyx_IpMAj=un]eS_]UruwRqPVUVUYY>]uZqRxauG\\x@EY@iqYAnIePqelOhS>qtPTpVqSUIN?`kH<UaLK@Hs:qxhLorQuCUUyyudyvNiVvhwX<VTateDqhPtquQwpY`IY>mWR=pbMUqtrbEUUDMPmTdtr>pkZxXixRryXksA:ZyAZXnMFIFWwKGiwvUt<`qy=jeuUl\\srivRiVI\\MoyNadLgXynUoDaKiYLtQPxnfr>_MgripuSOgtPcTYuDiyI^obU>kqrIkwSne;RQm[I<;BI:BqEgOesRUx>aIEge;jfFTdU?NNJJEZb::::b=yUN[IaoB[iyq]YFwwgcGoyurwilyrDQhhmI;UEh_w?sdkOw[AuEArBUb^SuToU<iHGMIuEUoYUe=i`edW[B<wEr\\K>]QfMMpTNf<mV`VcTqHQuRQ^MWtfwnkxpboooVawHbEqlLfufNc:AfvWnEabRVvwV`Cyv`@ao^tnVwyp\\roeuvaWvii?coF[CgpmawYAfui^AysBXfPWv;HsAisMAai@chx_Jgtiw_vHc[Aeh`ayFoc?woFaRVcog^uH_yVfsHyAwle^mmqmR@vmYtZf]_`<^<Fiaari>kc@nsOmhvkfvggP`=V_jQrGAej_rXV[KPsc@vwov]Q[tqegFxeGuBOyHWlZnyJArmqwjF]g_\\FpkInZ<?[[vc:>\\GqrOyin^tnXawObFabCnkn__kqsCwhFvrf>eMxLmEUsv^WxV?FIsfYMuMYrECugQIsmevYHVkCAUeHkEcEy@qioKyiyTMUivkcZmT`u>hENHa>NlbwnG_[PytIfgmw]QtYmuV[VJKilqUd=XjoyZ?F<UrewswcXyIY<wd[?C[OSroHVQeKgwg[vOEDrmhyQtx_CPkVsmD_ye<QG];eXuBlCyy;RiwFcixHiDgmBiYf>mXaqGici^yhegCsmU`yI:KHPIxiiGH?YBYhLQdlyI:gucKHxEv_uyV=cdgHwUYG_yq[IUYID?g\\[y=GIN?g\\OXvWBcoiUcVuQRUmW`sG`WrFIFBsIqSFY;wF;Uwqh]eIW;ysES?qwG?XrOgrQwjYRKwdNMUCGIwmsq]bTGryLOU\\vZTuSupRlyc<P=aMq=jppuVywB=V]QPK\\tb@rCEs^LLlEsvLlCaVLDyadQgdY>@N[dlO@txyo[ayTllIylMwntPexPxuwqlQxjHd?g\\A_pxnuliclNxu>yNWp>O[thZVqelFboWZQiv>^h^q[SyZKYfLHa\\Hc\\ghrgu=W_c@sZOiJViDXxt?wvw^b@`s_hc@eJXk`Yua_pvoZ;_w^PjlNix>Z<ytPn`ITHgxt_yy<RypMkyrAhQ_@q`]xPHplxmTDuyplIQsWqk`LkbtoV\\Y:UoEhRqlNW@lUEo[tO^pLwAQTERayJMAOh@Qa]nnMWqXwHDxfmyhuOcMWELVBLUQYTqEsmepBuX;\\nXHrwdSoAv[eSSEyeuxy=J;qqE`jlhXRtVRMYLttVutxIlOmY@ePNDtXIUw]uO@WYtKxUnhLZ\\XwqTTmS>qXQKtq]ItYT:kramYS[x:sYAw[mqnZWnav^^>:MHC[I:Ab^MDrWRwgHToS<cwDqeX;Wq]vxkwv]nY@TkdMIqw=`KPpqsdXYyi[yutywJAyxGaHQ`vyq=^gDovbpy>vpyxibvxiqpuiiKfbswk?`yKwy:>[hisy>dMpy^vupG_Rxy:vrIXyanyRXyyAZEyaqyaOQyoWiRaeO_aGg`LWmyEZ`q;UVcPVcQonxMvuK`\\LKeRneM;eRNN:::::BhuwJODi]WvIS[EEh]i;EGd=CoCYNeBoget;WyWvsGiAsDLaekosravkSdWefsQycMiowFE[IigfYEby=H^Oi>AVWCYPGWvgyLYv^[ClUxmIR^Yv_WWV;dA]VKcj:louhRxdOuEOYHSL]vYLURlmwmR=ho\\HlKHrZ=S;]jc<V<Hmr^ekygEpeDybLahSxZpqjAvmk?jEAg^`fj?il>\\;O[r?Z@pgpVojIl>?lAIpm^kPh^RXpmV\\L`sI_^LHc^NxC_^mqe`FgT`_tnxNoqyVsxI[mIqPahjHoKQnwyy:VsxA[?O\\=o]>qsl>ePPfFasHWck^aLHc^VLHs`uM?iLlikppwIYjN`mWpU`qyi\\n=UoUej]iVImMFUp;Pl>dX>txMIjKxuH\\J<<qsInTPu[iWhXvlyvItWhLXBdQStSo=QrtQJ=X;YJLUOyxTLInOio<IplyVIlnS@JCMrtMjuHo:AsiuR<EjW<MVytmtxa@XxyuQixauXvXM@iTlPoXqrohvAXLOixElybqyexocPRNuTI\\nJIM\\iulARE]peaKh]v[\\l]=Q^PKX<w`qPrTyeAmvIq]YyEaM<tK@YTWmSHxKN]MJ<RgW\\UwmKQcr_iAI[tOhLwnLw_OWpG?enAk^qkbOlRgmXw`JOsdQhRn]>p]\\imRoiL>qmahRFvgvloph:`kwgtA>_wvy:nhMwmIamPivvgxRWis>qpwaKHhrHe[I`o>`MquLFgvim<`quYdypyNit`OqPgu<ni`yuVPjZPx=Aosyksf]Nw^_xgrwoKG[egyQx]lfu[VxBW^^YkZ>`]ft@`dnoy\\n[QwZRxoEWZAolxFtoYuJiymOrxa]hwcrnonht=gxQ@wxHf?_\\QGiuAdKgbN>ZLo\\Pp`CgoRi_>a_^>kL@bVYaVVh=@t]Ao^vh_Pn=P]nI_\\I_DgkO?iCa`QYlwN[@qxgnb@Y]rX`_Qs[@jfgfIghr>w;?s]Fp@^oQg\\[is>GgtYkUGcxQnoqrH>bCn_kVlX`s<voXGn:wZkwreoePn^IPpWPqnwaN@qMX^ePl`Y\\<ycO_qY?iwxmbayJydXPgMfyiXeNq_lfrvWvLngdQnk>pIHfrHaYvwaGoonuXguAGf[Ghs?_]_]K^`f`\\lOb<pcw>yix`pHc]npGhfgOxgasI`mhyg\\IahIcCyswhh_AtrynlqyyXZhaqb>ru_cw_gUOe<o`XOpy_vYpuE?cFa\\^_v^AJmBCwF:;bVMDI=bqGFRAoM>:L<DCJW:::pw=f_UQenHgAOmAOwVVd?AafWjGvsyNifpqRvxmiiLPwxAcnf]>NuOfqw@dh?swaus?s:x]JIpWvchWjFplYQnD@xditOHem?cxqfFYpfnc_GkPX_On_cWstQpfyl>g\\qHvy_\\yOruVpI_t^vy:FkqfuDpfyFx]qyCyYGgIyI:_ymuymeIXcfOkIIEEMUcMkEYiXV;UFeIVeTYEwIofuqUMebsws?]yKsyBqGGuiJYDxaVYkhcAuy;bAyCuyfxAuuyI:Ssylwy=je`xdYYFl?:Fl=prLkdBxJ?]H\\LJOK:::xVWYWthqHTn@dmsQoRYUYysqHspPM[MLCupWXOoHsCES>\\Koep\\QyxusFYpLPxxmWETsRIXxHW^Il\\`f_wk=^^;@yJiZDPvoi[dNxAarXh\\PXv>Q]P@nAXdK`bQGdUQo=pxuvmRHikG^IA]eqkIg]kntRwuSQwpGhXAeWGrqWg`nhG_Z<`bfO\\H>]j?h;w]?HitIwtihaXkvv__vm;xij`ft^jZhuso\\c_qwOl]avFQ`mVh;av]gveamJwZ^xdWNvYq\\w`lI`ncQ`IfwFv[xVv;nlKAcBAvjafZNjN>x;^;UuOssP?yo_W^cYaGSJuYb=vssHR_cpMS@sbASB[[bJwnJbdsIC]DC]CuStrES\\GEESHkCyfaRlCc^MDI_VLssoMf`Gu\\WRievEYfvyQ;mQqQqHmLOLQnxuyDyyS>CD^B]P<jaNLCcvVxIOnDHy@Vuqwf;QsHociAh\\Pkc>[bNN;rmeHwKVWQEVSGYmwrMh[;eF[da;g]OIV_sH]In;vKYBGasPsTIeGmwEQ]YyEim=t;AWDWycIJouJ><LwPnmdXwMNWPUVUOYlorMx[=mF\\la<o]PQV`kH\\Yn=nKXu?dRuuQluyIhVwuYXuyoIRvdVUQng\\WemUREYwttRyq`ykdQqtamy=j>lOFQuWhUKtn^IxE\\J:<XS@XhHse=skXvqLStyxdmWhQnnhpTlvpEUF<O^qX;=QJ_mINgZiwTfgi^rpOb_Q]cVfRhbdF^HixM@_^p]qF^\\wnxYZMQhZQgrWoJW`VqoQH]@^^Ef_@YapHb?wsfWfk_]XVdkP^qxoApxoXvgOmuHyy?rqput_e??lfXuCHnFV[H?]>pn^ppqPuyWjxooIYdLVgSxohhnw@qWWlGOj]os>OgA>[I>naAuLxr=>a`Ht?OipVc>oiqYj<Id;If[qjZhoBV__^vNFd?wZBGd?_<]TKFuM^sFpo`YbNQaVN`X`rX^rXFboi\\VAwTGnOahiq`?gdrHkFYddvv;njBV^wNkO`g^Wvrns?GhOVgD_tHVlchn;A^U_sPW_VpxXohpXigg_LPigg_QYZV>yTpaPimPtUQixcHyqIkwSAwIoQhiaWKwewgvdWxIMeYQgnuhMIVkiY=wr]ubhCYYWWWEF`sRR;dE;h];I[OsKAgYIr^Ge<_cV_EJlJCyN:<jVLLIwwToyg>qInoUOrNoy\\Yu]^]QP`x@Z:VhVhrAaehayoahW^:puX;rAZ=`KOH_Ay[AxcWchyqihlyHvIil[aSeYk<]ynDPotLoPWHmskPwgqw`hXLQOXYUR]PW`:jB[:ZtnMriET?EYoQgD_gs]VxGTSmfRaEESTfkTdaeMyToiFSoGB?g\\QsFCFD?g\\;rDYejwIDyI:CvWGuaKWLyQCxpWMK`yqkYvxIsy=J`pqy=jlyswySoAYNtTXuKSTTEXTXtmo`ug=r]QwZQOuMSyipVqXTXOF]yiPvI<YAmxcQy>xMkqnuEpFyRx]qy=JSyqnyrYmySyimgyYwnQ_u[GhNGxnftDwgxIZtqbIF]Ew\\Cgd^xY;YX[cb>ndQ[bNn:P[bNN::ssy;bPyI:]vR?y_uygyI:aHUeBnku[wyJwv>yI:[GeyfxETWot?od?YVYKWjKgqMeOis?[XU_iUGugId^usc_Uu?eF[SLASAURLaEcMyggwwgswoUYCGvuDHqE\\EY[mdS;E??BrSVF=B>?rYoWIEjsdYxdQDeuIerEinWMUUyswEPSxvtlpcati@ug<qDLP[tjrtvwtkVHxQLVUuMPXSb<YpYniDWKes`DN\\DRnLq=UjETmuxMYdkjIRjtPZIlNMJlEjM]uR=uSIWPHxS=UTERcUWXlX=]J\\]pVMLH]LjMPCyQGxTNaxIyPYEWqlqqylwumpuTupxaaSFQp?upsXVwmwmysWurv=JHllipjT\\tk\\WIMLRUv_DKgmO@mV\\MH]e^MDC_VXDcdPeqWjoVsuiwTWuuYiHwkuqAUugyUSmwvaC=_duIxaIhxsxRyvhwFxwreeTuSYUUyCqg`KbwMtWKc`aEhufu]rRIbayfDKsraxoeCk_IuQsW[uKuFEIW;IsWUDQ;yI=IQQyaciFMuqkYDyeyKDeuy<=h`Gyg=YuacOwiqaXbqYWCwOwsOgyPgWmKy@WEY]IaIU@;xeiddgi?gcxGUaUURIuAivTQe>Ad<WuCOED=bKYtCtJTyuS=qIIypijwIl;xY:tmBUXGxr;Qm_ijpUlgiywVluQbgioqxIkgv]I=_guIpaeYPIpAqUI]WWxKruttxVwaKTxXxMkYyY:LlexqrHpqXqXLtcYVYin^lNbqK\\mPsprFlmt`yhXRYtUViTDxQm@xYXXgyJpmrAlYwYNDINjqVsxOBtwnymgeWrhyTLtEvgpYevque_suHhaIxIx^svsuVq]gmI>yQOaaiyFNmqoyDveye^QsiQt@kUwmregHIuTMcBVKxxYFmKFQKwkWD=YVxqi<]wKgiUabyuEbwIl;xy;rmCWXGT[;YmauP[iwmvdyuUMEnuih_xDyvDqYEqhScY=igIkemaC];YNSGxaCQ_HEAUhwiqaXcyxWUUUiwxUsowBWMh?SYxIicsyrwWFIhPcYYQBMwIk[iwmFcmiqiEpUeBgwvgUuyXf?buGhMaC]AiCSgQkxpOI>SsG]Tx]Fe]GmGbr[SvoGlIv]GTOwCxIi\\ysf[=IbwGt;wYYAslewaAfpWVhMEssDx_VkKB;SSfMeMuRJ=IZGcV[sK[tK=gt=B@]GYACoWEIQDdMenkeaib_QCTWcqEIw?IMGgOeFVITaGHIyfcKB:;rDshtoGPqxkKWmwUf?itKubGvKshYCeJEiKoCVCuYYHpgTn?HNSVXAU?AUo;hmkt<uUO_ipgygQdpgYuquDqxXwRLyQ?tmwuY=isylyDXuy=jIltxikjqKuytkPlamYLTqrm`sppUiyThsYp^aWkp_i[yt`GhUAaaiougmQWpkxpMAvbgg]Ox]Ig^?mG`r_avpGlIqaf`swWpAa\\xioAGyIWCaUFyI:yFe]YMIUrubw]vRurmsICDyqiUUUugqiEykt^fEphvWvMqikwuRVvg@gyOrIpqyAZ[pnYyy:fZgwy:vreqtiagggxBn\\U>ovAsPAe`YZk?]rgu^WbAYndvmvWh?Ae]PwNyiNxaqX`YFytysFVm[i]nqe[NpLyi[Y^qxac_pXxvGqyGygQPsrwdh_ahYhayfsVvi_ikInye<jG;voMWmFWxvWb_Wos?uui`^pxXqdYiq`aqgVqsVvXncknkqohAQaNfiTwklyjpqv]wy:vaSGvTx`<Yagqe@YcY@yBgw\\IuqWhgwpui`UpaFwsP^wsYrh`s]qpkwsTg`YajqOuavjohaUoyLVasoq=IggvsOhyTXsyPfPVuY@a]Aa@AheOufawg_xrQ]U>evAqTIe`V^kGasg]^XhIYomv]fGx?y\\pq`tqmWXh[GiYFmeghMVrlng]NhjF^@xb]>^X`lwOEjkZ^ymjYniyqbIgqxy:FrUwikQyHAqrIbrOqwqnHpu\\fpoWqn@qrp_nWr:X^bwdhwuu^msquvhgiqmwNtehqG`qT`kqfwXng[PkBWfwwr_ybb>e]wn`^`viqGy]PWnvAnmaq;AwdYpDa_xV[dodT^jQxr?qdqydGfkiHh_XpNNr?@s>YvW@nF^mX`qlYh]ocjqfsxiwWoUwiiSnyqmpwPUuqmxUuMm@P?qOfIYvyY:hO@IquIqiIjdexXqu@qULYys@NI`VQPxCtnuHkXEVP<psIwlQNHdQwTxSus;pjbtWbl^dAyFn`\\^eOAfUPcXIkfwl^Wq]^sovu@VgTx>p]uYIqFugc^sXxyTpWuhgYBUUhaimaC]Ie;cwI=IQ^X>YtihxuWWtynpviacHwxvhMpxeIcg_qWYqpxg<WqkHlVxfr>sgP[I`wVy^vYy@waSA]YFynykb^tvG]h@eYGgpvuUQunwmTy\\ggguXygvrQ@k_wlp_axyiOYfVfIgYj[xy;R[aeeyEnMxcyErEwy;Rx?shqy\\qrXmWuGcaucvodLGEZWyBAE_KUlAyeOHumSweYkktbqyGMry;bI[xYCERyus_HIAgM[A:::::rJwY?WXhyI:AdCuvy;bZivyLX?yxpmxpv>o>:WqkXZYP?RG?u]SIqI[;gyKHjyAZY@clikEFrTpV=qST?@D:pFWEY]IaIU@Htb<Ym`ujpQLiwyx`LyibgeoppiaWwbQ=c_uDpaYxyI:eD]]uwawpIrnSIEUEwUhHohjWxIWcogHCGF?shMcHN?B]wfMpKn\\uRYuWuScapkywLLTM]PADXU`M]lRIeMxut[ysilobpyGMry=jI]pYDURxmsaXHXJxilHIQyUr`hmygZivy:FsOv`A`xyAZO>wtikYqjgixwq_EWge>ghFfc_pcX]EIeTgdlalEFj?xe^FlLHhyXZD>nQ?nPaitvfOPvUfuUosIQug?^pPxphyYI_`igSyssVxk`kkwpx@iTqkPfk@furNuaqbYfZAXrp@wAqlwYkJH[Ppu_>qLHaa>[>vkT^\\P_glObL@cSfwMxkMOdKgbng];gbN>d;fbN:::XjYDXsDYh]XWxqImMeXYwIr[@QlmnbiMKhwa\\l:<W=yOIMmY`lFTvALJ;]QjluedMuysmyvPpU==TRiwvIYTtTNUWbenZXqLhsmAsamVaHm:=V:\\PodW_dpRANyIsXpt\\MUYQqXmvGXQ\\iyf`j:PWDQxHXWmIouEUR<NKpmUPNG\\PmhowauMeSjmwhxNNxrthvvDPRlKOPZdvrGHjx?vHQhUAjsfa?vnHXs;Q]yXui_nuptpiiypsvplB_vYyfffspp^\\GlxIxNfkD@q=VZD>ci@bhxiH?xVP]voxyFxknqr`pMyq]QrDygeVsoHyFVgnPoA^g@_s=XiqvZaf_<PaDBD?g\\;:XXxuNihoHYjaHymeRiyiJ?gh_aCPma^fUGg_AZt>\\EYx@yj_Y^rFrZAlI_[QNkaqeMaysivq@pNq\\UvixnfOhtTNuC>ch^vm`ilIasIk@Ahr>ZGf[UGcGodbvaLyfo@qpxlHypsXjh?yYXg[>^tNpVXnt`yDqipqbB^ZAonbYnG_[Eyiq_`maeUVkchvKnwsxgfnb=fj:?n?>ekApi^uSnsU?hAv`dxryvjiGnYxbMhdOipRNfTPwxqtEGu_Wx[@\\DydqyfknrIQa@a\\@Okr?hehpVG[vf]<FwQq\\Py\\kAi<h_RGu^GsdPgGNaWaZbf^KHdaglJnw^?vZayraeG@uJYtvh^_VjVqgkq]mXhOVsByxKNsZWbeNaga^Ca]E?^Z>fcvdUNbb@]DfZVWtnY\\c?oEXywpduYdt@cT@]X_w<oqLGaL?vBVn:whNvcw`mg?]@qc:o`bNnDDDrDqfo?iHYf\\cWeGsTQFhSYs_whmWWeWh_VqoFLwXq[t_UV_[G;YgvIy;;C^KD@MyDYSO]hKEWVYuWURywxameUYf@sdpKvlmeUcdh]bBoCrcvJsvSEI@;c>Kb;wT^MgqqDXICNuomLWqllLLwKDr@PVLaSjtSdtrX\\WPlvdPkulkRmMHEssxnZ=WQpsrppjxqE\\RKPw@US`dSM=tcqTbEN;aoDTkv@OATXatjAxv<]vhuR;Iw[TRa=vfXntXQlEm`XXk<n@MMCuuuMSS=R_iy?ASR]tGtf<iwIxcJic`PninwoYegqccQ^bGfuGpDFyBgvE?j\\fk;^uKoapIhnXfSFAkhbOFD;bb\\\\hxgU?kdqadNtnHmhp_]YpPPshivPqt`YcpGg]VioObXo`P?rLvqEamVNj;?^]_nfhqQgbTfl?iqVy`qQiwgvt`acWhdW^gfvsPdbabBXw<HdHFhY`lZ?jB?^N^ynveJ?xNqxqYdIQ^ghugAmMps[?^DXaCPfIou=VqjgbKwquFkSv^vvtifaO`tTwfCxgnHaoVs?xlTfbNXgcxcjOwxyfOh`DI[^GySg]BHrevkmp\\HVo[V^rXtn_lLAn@@]hvfbWtGIg=fwx^hlxaRPxpx\\@`_VGvpwoHqiVgZUi]xxjGvm@honWaeWorPfnxpD@[hO\\:g^Y__:foV@fY`lL>[dFi>>\\B?nFvy:V[U@chx_gO\\QIem`q>OkCggoXcqQq[W]Q>[dacl@o>^O;rZ_iv]Cgwf^_GwUG?Mugir?auQuhtir_KR^uWm[H]ic_Ef\\;S>?gE=jVTVyHPC=N:dPb@j\\L[;ZAv`]q\\xPkIycXPtxYcRWlMOpSOl_VrFo]da\\TYelhga?s=f_AA^hodkPvSqv=PbK_[l`bagqmpppgkDxpQh_FIdr`[sNdO?uh?]]Fa>>\\G>gdOifOagPoUosLQ__^rQ>Z[@ZhQkOglA?^kIq:naSIwPYnNapNhtZOmSnwa?eYQsbOrgo]FGpy@mLpoQolF>\\[ypi>sx^eP^u;vl\\`bnwwONgt`cqv\\lSkEUT_u\\euVEsjSc^ucjmw=AsF;E\\aVsWh;MB:_rV_hOwT_?W]gcr?iuQuxugJ_Yr_rGmgh]b[_In]GK?BGEDjWssksmShVKD:UbL;BD?g\\;BD:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::xyf;:1:\"\{\}

EXERCISE: Make up four affine transformations and apply t3 to find the 6th approximating set to the corresponding IFS attractor.

EXERCISE: Plot the attractor for the IFS parameters of the Sierpinsky Gasket starting with a "small" set

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn