{"title":"The logistic map, as a model record","parts":[],"pages":[{"id":"logistic","title":"The logistic map","part":null,"status":"final","summary":null,"desc":"The map $x_{n+1} = r\\,x_n(1-x_n)$ on $[0,1]$. This page exists to show what a record looks\nlike: a figure carries the code that drew it and the numbers behind it, so the catalogue is\nreadable by a person and by a program.\n","figures":[],"tables":[],"codes":[],"content":[],"sections":[{"id":"orbits","title":"Orbits","desc":"Four orbits from $x_0 = 0.2$, through the period doubling into chaos.","figures":[{"id":"orbits_fig1","caption":"Fixed point, 2-cycle, 4-cycle, chaos","code":"fig_orbits()","params":null,"assets":["assets/figures/logistic/orbits/orbits_fig1.svg"],"data":"assets/figures/logistic/orbits/orbits_fig1.csv","table":{"header":["series","x","y"],"rows":[["r = 2.9",1.0,0.46399999999999997],["r = 2.9",2.0,0.7212416],["r = 2.9",31.0,0.6524127088188063],["r = 2.9",32.0,0.65763406195249],["r = 2.9",60.0,0.6553017122858438],["r = 3.3",1.0,0.528],["r = 3.3",4.0,0.8239266326138736],["r = 3.3",5.0,0.4787360710553407],["r = 3.3",32.0,0.8236032832158181],["r = 3.3",33.0,0.4794270198034119],["r = 3.3",60.0,0.823603283206069],["r = 3.55",1.0,0.568],["r = 3.55",26.0,0.8872805955063953],["r = 3.55",27.0,0.3550487782219521],["r = 3.55",58.0,0.8873667058031404],["r = 3.55",59.0,0.3548119750850427],["r = 3.55",60.0,0.8126675528455927],["r = 3.9",1.0,0.6240000000000001],["r = 3.9",9.0,0.9742156868513789],["r = 3.9",10.0,0.09796598114189214],["r = 3.9",55.0,0.9726111395952336],["r = 3.9",56.0,0.10389097184892901],["r = 3.9",60.0,0.8814209848341189]],"total":240},"comments":[]}],"tables":[],"codes":[],"content":[{"kind":"figure","id":"orbits_fig1"}]},{"id":"bifurcation","title":"Bifurcation","desc":"The attractor as $r$ sweeps $[2.5, 4]$; the accumulation point is near $r \\approx 3.5699$.","figures":[{"id":"bifurcation_fig1","caption":"600 values of r, 80 iterates each after 300 discarded (a raster: 48_000 points)","code":"fig_bifurcation()","params":null,"assets":["assets/figures/logistic/bifurcation/bifurcation_fig1.png"],"data":null,"table":null,"comments":[]}],"tables":[{"id":"bifurcation_tbl1","caption":"Where each orbit above sits","code":"[[\"2.9\", \"fixed point\"], [\"3.3\", \"2-cycle\"], [\"3.55\", \"4-cycle\"], [\"3.9\", \"chaotic\"]]","header":["r","behaviour"],"rows":[["2.9","fixed point"],["3.3","2-cycle"],["3.55","4-cycle"],["3.9","chaotic"]]}],"codes":[],"content":[{"kind":"figure","id":"bifurcation_fig1"},{"kind":"table","id":"bifurcation_tbl1"}]}]},{"id":"oscillator","title":"A damped oscillator","part":null,"status":"final","summary":null,"desc":"A second page, so the catalogue shows what a multi-page record looks like.","figures":[],"tables":[],"codes":[],"content":[],"sections":[{"id":"decay","title":"Decay","desc":"$x(t) = e^{-\\gamma t}\\cos(\\omega t)$ with $\\gamma = 0.35$, $\\omega = 3$.","figures":[{"id":"decay_fig1","caption":"Envelope and carrier","code":"fig_decay()","params":null,"assets":["assets/figures/oscillator/decay/decay_fig1.svg"],"data":"assets/figures/oscillator/decay/decay_fig1.csv","table":{"header":["series","x","y"],"rows":[["y1",0.0,1.0],["y1",1.01,-0.6978581459440829],["y1",1.2,-0.589212265594738],["y1",2.06,0.48367935685777463],["y1",2.4,0.26263166442548863],["y1",3.1,-0.33527470948039756],["y1",3.6,-0.05512246043537944],["y1",4.15,0.23240205819636064],["y1",5.2,-0.16108237628206998],["y1",5.99,0.07833886542625856],["y1",6.24,0.1116466895584261],["y1",7.19,-0.07368649781719644],["y1",7.29,-0.07739318817463285],["y1",8.34,0.05364490394923791],["y1",8.4,0.052746198341901494],["y1",9.39,-0.0371811754202073],["y1",9.6,-0.03004564756433838],["y1",10.43,0.025772434453556686],["y1",10.8,0.012635439250213156],["y1",11.48,-0.01786482946180235],["y1",12.0,-0.0019188893380395144]],"total":1201},"comments":[]}],"tables":[],"codes":[],"content":[{"kind":"figure","id":"decay_fig1"}]}]}]}