# Curve of indifference

Classified in Design and Engineering

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Mandelbrot set,except zn+1 = zn6 + c:%gen a grid of pnts in da specified complex plane & determine da associated c val(simply x+i*y)%Initialize matricies for iterated val(z)&# of iterati before blowing up(k);everything will be done at once in a single while loop%loop to iterate da grid&check for divergence.loop stops once N reaches Nmax%Any k locations for which abs(w)>maxZ at dis prev iteration get assigned da value of N(indicates rate of divergence&to color code)%If any k's r =to 0 sets dem to da final iteration#Write a singl line of code dat = a bin seq dat bounces back&forth between low&high vals.#defineTRUE1#defineFALSE0 describe da backgr behind da 'atto-fox prob:Predator-Prey/LotkaVolterra:[tM,PM] = ode45(@(t,P) someFunc(t,P,k,L),tI, Pinit);[tM,PM] = ode45(@(t,P) someFunc(t,P,k,L),[0:stepsize:10],Pinit);a.Expl da main purpose dat these lines of code r meant to accomplish.B.Specify wat eqs r to solved here.C.Indicate wat da diff between da 2 lines of code is. Explain wat da 2nd line is doin:1-solve via ode45,but need to use an external func to define the ODE%numerically solve da Logistic eq=P’(t)= k*P(1-P/L)%k,L=user inputs, Pinit =% initial cond at tI(1)..tI= [0 10] =% time boundaries...stepsize —>% for RK4.% RK4&Eulers method)//counter.RK4 solu.Also store away Euler's meth val//keep track of t for plotting//increm counter/Lagrange interp of data pnts..spline interpol of da same data pnts.fig2,shows an ex of da cubic spline curve thru the same data pts.in fig 1,da jump in the height of data pnts near the middle has a strong effect on da interpolating polyn curve near da ends.Cubic provides gd balance betwn simplicity&capturing curvature :A tridiagonal lin syst is bein solved for da info needed to describe da coeffs of da var cubic polys which make up da interpolating spline.Spline uses da funcs ppval, mkpp,unmkpp.These routines form a small suite of func for working with piecewise polys.Basic alg consists of:Fitting a cubic poly to a limited /centered grp of data pnts.Set var prop=at da end pnts to guarantee smoothness(piecewise continuity).Slv da resultin(linear)eqs(which typically have a nice matrix form.Matlab has a separate‘Curve Fitting Toolbox’