Plotting two different equations on the same graph/matlab - matlab

Question

While I am able to plot my FFT( fast fourier transform) plot(X,Y), however I am unable to plot my fit line f(x) along with my FFT. The equations was gathered from the curve fitting tool, I took the ten best fit and averaged the to come up with equation f(x).
what must I do for f(x) to be plotted with log(freq) and log(Pow)
code:
row=69;
col=69;
colormap gray
whitebg('black')
iterations=10^3;
Next=zeros(row,col);
laplacian=zeros(row,col);
critical=zeros(row,col);
B= zeros(row,col);
lums=zeros(1000);
flw=0.5;
u=0.1;
crit=5;
%bns=200;
bns=1000;
for k=1:iterations
B=B+(rand(row,col)-0.5);
Next=B;
rns=5.;
for i=1:row
for j=1:col
rfromns=(col+rns-j);
critical(i,j)=0;
if i<=2 left=row; else left=(i-1);end
if i==row right=1; else right=(i+1);end
if (j<=2) top=1; else top=(j-1);end
if (j==col) bottom=j; else bottom=(j+1);end
l=B(i,top)+B(left,j)+B(right,j)+B(i,bottom)+0.5*(B(left,top)+B(right,top)+B(left,bottom)+B(right,bottom));
l=l-6.*B(i,j);
laplacian(i,j)=l;
bfromns=bns/rfromns^3;
if (abs(l)/((abs(B(i,j))+bfromns)+0.01))>crit; critical(i,j)=1; end
%if abs(l)>crit; critical(i,j)=1; end
end
end
for j = 1:col
if (j==col) lum=0.;end
for i = 1:row
if (j>1) Next(i,j)=(1-flw)*B(i,j)+flw*B(i,j-1); end;
if (j==1) Next(i,j)=(1-flw)*B(i,j); end;
if (critical(i,j)==1)&& (j>1) Next(i,j)=B(i,j)*(1-flw-flw*u)+flw*B(i,j-1)+(flw*u)*B(i,j)/5.; end;
if i<2 left=row; else left=(i-1);end
if i==row right=1; else right=(i+1);end
if (j<=2) top=1; else top=(j-1);end
if (j==col) bottom=j; else bottom=(j+1);end
if (critical(left,j)==1) Next(i,j)=Next(i,j)+flw*u*B(left,j)/5.;end
if (critical(right,j)==1) Next(i,j)=Next(i,j)+flw*u*B(right,j)/5.;end
if (critical(i,top)==1) Next(i,j)=Next(i,j)+flw*u*B(i,top)/5.;end
if (critical(i,bottom)==1) Next(i,j)=Next(i,j)+flw*u*B(i,bottom)/5.;end
if (j==col) lum=lum+u*B(i,j)*B(i,j)+abs(laplacian(i,j)); end
end
end
lums(k)=lum;
B=Next;
%Matplot(B)
%if (k>00)
surf(B);
%plot(lums)
%view([0 90])
%pause(0.001)
%end
end
c=fft(lums(129:iterations));
pow=abs(c).^2;
pow=pow(2:(iterations-128)/2);
freq=(2:(iterations-128)/2);
X=log(freq);
Y=log(pow);
%x=length(X);
x=0.6:.1:6.;
%Linear model Poly2
a1 = -0.155;
a2 = 0.2154;
a3 = 15.1;
af(x) = a1*x.^2 + a2*x + a3;
%Linear model Poly3
b1 = 0.01805;
b2 = -0.3687;
b3 = 0.9874;
b4 = 14.29;
bf(x) = b1*x.^3 + b2*x.^2 + b3*x + b4;
%General model Power2
c1 = -0.09124;
c2 = 2.179;
c3 = 15.34;
cf(x) = c1*x.^c2+c3;
%General model Rat02
d1 = 727.3;
d2 = -3.447;
d3 = 51.6;
df(x) = (d1) / (x.^2 + d2*x + d3);
%General model Gauss1
e1 = 15.01;
e2 = 1.346;
e3 = 8.152;
ef(x) = e1*exp(-((x-e2)/e3).^2);
%General model Gauss2
w1 = 1.737;
w2 = 3.46;
w3 = 2.333;
w4 = 30.03;
w5 = -23.14;
w6 = 28.23;
wf(x) = w1*exp(-((x-w2)/w3).^2) + w4*exp(-((x-w5)/w6).^2);
%General model Sin1
g1 = 15.11;
g2 = 0.1526;
g3 = 1.428;
gf(x) = g1*sin(g2*x+g3);
%Linear model Poly4
h1 = 0.0179;
h2 = -0.252;
h3 = 1.047;
h4 = -1.97;
h5 = 16.23;
hf(x) = h1*x.^4 + h2*x.^3 + h3*x.^2 + h4*x + h5;
%General model Fourier1
m1 = 11.05;
m2 = 3.31;
m3 = 2.104;
m4 = 0.3644;
mf(x) = m1 + m2*cos(x*m4) + m3*sin(x*m4);
%Linear model
p1 = 0.815;
p2 = 0.1061;
p3 = 8.904;
pf(x) = p1*(sin(x-pi)) + p2*((x-10).^2) + p3;
f(x)=(af(x)+bf(x)+cf(x)+df(x)+ef(x)+wf(x)+gf(x)+hf(x)+mf(x)+pf(x))/10;
plot(X,Y)
plot(f(x))

Answer 1

Matlab/Octave therefore use the hold keyword.
If you want to plot several things on one graph, you start your program with hold on, then execute one or more plot command, and finalize with hold off.
Example:
hold on;
x = -10:0.1:10;
plot (x, sin (x));
plot (x, cos (x));
hold off;
Documentation: https://www.gnu.org/software/octave/doc/interpreter/Manipulation-of-Plot-Windows.html
As the documentation describes, plot will normally call the newplot command, that removes the previous plot result, with hold on; such behavior is prevented.