FthmFDockDFHAMaccdDChDcCncdCCdsCCaxcrFnTb@FnIOPalatinoTxEnFnIOArialTxEnTblCKCmpDCmp TblC Case Table 1KCntDsCnTbCnÕCmRfÝ€CTmd†TablGTbHlTbGm(TGhtdbl runl@WÀ@4CTslAtRfa@4@9CDNdCDclCDFlCDNdCDclCDSrCmRfÝ€DColKCmpDCmp DCol Collection 1KCntDsCngClCnÉCmRfÝ€InSt7CoIn @7@g@r @zÐCmPnCmPn InPmCsPnìInPmâinTMaaTMÒTabl_TbHlTbGm@TGhtdbl runl@RÀ@N@a€@4Tabl_TbHlTbGm@TGhtdbl runl@RÀ@N@a€@4CtPnInPm inTMDsPnìInPmâinTMaaTMÒTabl_TbHlTbGm@TGhtdbl runl@RÀ@N@a€@4Tabl_TbHlTbGm@TGhtdbl runl@RÀ@N@a€@4MsPnìInPmâinTMaaTMÒTabl_TbHlTbGm@TGhtdbl runl@RÀ@N@a€@4Tabl_TbHlTbGm@TGhtdbl runl@RÀ@N@a€@4ÿÿÿÿ?åUUUUUUCDNdCDSc Coll arithmeticCDNdCDScCDHlçClCs XAtLsÝCCsAAttrCsAtCCsAXaPrLsSPrLRplus[customfxn"prev"[id[comma[string[(**)"a"],string[(**)"a0"]]]],string[(**)"d"]]CCmAAttr CmAtCCmADisplay PrLsSPrLAtLsCCmAAttrCmAtzCCmAOriginPrLsSPrLAtLsnCCsAAttrCsAtCCsAxPrLsSPrLCCsAAttrCsAtCCsAyPrLsSPrLCCmAAttr CmAt&CCmAPicturePrLsSPrLAtLsCCsAAttrCsAtCCsAimagePrLsSPrLCCsAAttrCsAtCCsAxPrLsSPrLCCsAAttrCsAtCCsAyPrLsSPrLCCsAAttrCsAtCCsAwidthPrLsSPrLCCsAAttrCsAtCCsAheightPrLsSPrLCCmAAttr!CmAtµCCmA_CaptionPrLsSPrLAtLs©CCsAAttr CsAtCCsAcaptionPrLsSPrLCCsAAttrCsAtCCsAxPrLsSPrLCCsAAttrCsAtCCsAyPrLsSPrLCDNdCDScCDHl %HmCAAtLs HCAtAttrCsAtHCAtwaPrLsSPrLFrCAHmCDFrCAcRplus[customfxn"prev"[id[comma[string[(**)"a"],string[(**)"a0"]]]],string[(**)"d"]]SApCAttr CmAt FxCAGmCmAppCSApCDisplay PrLsSPrLAtLs OrGeAttrCmAtPOrGeOriginPrLsSPrLAtLsDHCAtAttrCsAtHCAtìxPrLsSPrLRelCHmCDNCsDRelCÐ@@@V@b@i@p@@@V@b@i@p@@@V@b@i@p@@@V@b@i@p@@@V@b@i@pHCAtAttrCsAtHCAtìyPrLsSPrLRelCHmCDNCsDRelCÐ@8@8@8@8@8@Q@Q@Q@Q@Q@\@\@\@\@\@c€@c€@c€@c€@c€@i@i@i@i@iIcGeAttr CmAtƒFxCAGmCmIcGePicturePrLsSPrLAtLswHCAtAttrCsAtHCAt²imagePrLsSPrLGnCAHmCDGnCAž`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€`€HCAtAttrCsAtHCAtìxPrLsSPrLRelCHmCDNCsDRelCÐHCAtAttrCsAtHCAtìyPrLsSPrLRelCHmCDNCsDRelCÐHCAtAttrCsAtHCAtìwidthPrLsSPrLRelCHmCDNCsDRelCÐ@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0HCAtAttrCsAtHCAtìheightPrLsSPrLRelCHmCDNCsDRelCÐ@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0CpGeAttr!CmAtUFxCAGmCmCpGe"_CaptionPrLsSPrLAtLsIHCAtAttr CsAtHCAtËcaptionPrLsSPrLStrCHmCDStrC·a casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea caseHCAtAttrCsAtHCAtìxPrLsSPrLRelCHmCDNCsDRelCÐHCAtAttrCsAtHCAtìyPrLsSPrLRelCHmCDNCsDRelCÐ@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ Arial@& ClOrThngCmTh•AtLsˆThngAttr ThngPComment PrLsSPrL LPart of a series on iteration, by Henri Picciotto www.picciotto.org/math-edCtSLCDNdCDclCDFlDCOrClOrDCOrAbIM$INMd.@7@g@r @zÐ@7@g@r @zÐ?åUUUUUUslidKCmpDCmp slidSlider 1KCntDsCnVSlCn¿CmRfÝ€InSt-CsInObInÿÿÿàÿÿÿàÿÿÿàÿÿÿàÿÿÿÿÿÿÿÿSlMdµOper GlVlNVnca0a0AXISaxcdaxcl0?ð¿ð@*@¿ð@*OperNVncMax_updates_per_secondslidKCmpDCmp slidSlider 2KCntDsCnVSlCnÅCmRfÝ€InSt-CsInObInÿÿÿàÿÿÿàÿÿÿàÿÿÿàÿÿÿÿÿÿÿÿSlMd»OperGlVlNVncd@d@AXISaxcdaxcl0?ð¿ð@*@¿ð@*OperNVncMax_updates_per_secondtextKCmptextKCntTxCn‹ÍThis file shows how to iterate the function y=x+d in Fathom. a0 is the intial value (the seed). In the table, the column a shows the orbit for the given seed. In the formula, prev(a,a0) means the previous value of a, except when there is no previous value (i.e. in the case where the caseIndex is 1), in which case, Fathom uses a0. This is a recursive formula, where each value is calculated based on the previous one. Question: how does the orbit depend on d? on a0? Follow-up: create a similar file, called "geometric" to iterate the function y=rx. (One way is to start with this file, use "Save As...") and make some changes. Use that new file to figure out how the orbits depend on r and a0 in this case. –>><0>>><0>>><0>>>>>>>>>>>>><0><0>>>>>>>>>><0>>>>>>>>>>>>>>><0><0>>>MfsS  SFmsCTbFCmpFNdspFFltFCTbF@d@ƒfram@U@@.CmRfÝ€ColFCmpFNdspFFltFColF@K@Gfram@.@4CmRfÝ€SldFCmpFNOffFSldF@gÀ@Rfram@qÐ@4CmRfÝ€SldFCmpFNOffFSldF@gÀ@Rfram@qÐ@[€CmRfÝ€TxtFCmpFNTxtF@i @z@fram@qÐ@iCmRfÝ€2xý