>> phi=(1+sqrt(5))/2

phi =

1.6180

>> format long

>> phi

phi =

1.618033988749895

>> p=[1 -1 -1];   %表示多项式 x^2-x-1%

>> r=roots(p)

r =

-0.618033988749895

1.618033988749895

>> syms x

>> r=solve(1/x==x-1)     %直接求解方程不用转换多项式%

r =

1/2 - 5^(1/2)/2

5^(1/2)/2 + 1/2

>> pretty(r)

/ 1   sqrt(5) \

| - - ------- |

| 2      2    |

|             |

| sqrt(5)   1 |

| ------- + - |

\    2      2 /

>>  phi=r(1)   %获取第一个元素%

phi =

1/2 - 5^(1/2)/2

>> vpa(phi,50)  %变精度%

ans =

-0.61803398874989484820458683436563811772030917980576

>> phi=double(phi)

phi =

-0.618033988749895

>> f=@(x)1./x-(x-1)  %必须用./数组除算符%

f =

@(x)1./x-(x-1)

>> ezplot(f,[0,4])  %easyplot%

>>  phi=fzero(f,1)  %找零点%

phi =

1.618033988749895

>> phi=(1+sqrt(5))/2;

>> x=[0 phi phi 0 0];  %x包含5个元素%

>> y=[0 0 1 1 0];

>> u=[1 1];

>> v=[0 1];

>> plot(x,y,'b',u,v,'b--')   %x-y是蓝色实线，u-v是蓝色虚线%

>> text(phi/2,1.05,'\phi')   %标识字符，不同位置的标识字符%

>> text((1+phi)/2,-.05,'\phi-1')

>> text(-.05,.5,'1')

>> text(.5,-.05,'1')

>> axis equal  %使x，y方向坐标相等%

>> axis off   %使坐标消失%

>> set(gcf,'color','white')  %背景色设为白色%

以下保存在m文件中

function goldfract(n)

%GOLDFRACT   Golden ratio continued fraction.

%  GOLDFRACT(n) displays n terms.

%   Copyright 2014 Cleve Moler

%   Copyright 2014 The MathWorks, Inc.

p = '1';

for k = 1:n

p = ['1+1/(' p ')'];    %p的6级截断连分式，不断循环%

end

p

p = 1;

q = 1;

for k = 1:n

s = p;

p = p + q;

q = s;

end

p = sprintf('%d/%d',p,q)    %q/p，相当于q+p/p，不断循环%

format long

p = eval(p)     %和上面的p相等，但是是十进制表达%

format short

err = (1+sqrt(5))/2 - p   %phi和p之间的误差%

命令窗口输入

goldfract2(6)

结果输出

p =

1+1/(1+1/(1+1/(1+1/(1+1/(1+1/(1))))))

p =

21/13

p =

1.615384615384615

err =

0.0026

斐波那契数

function f = fibonacci(n)

f = zeros(n,1);   %(n*1的零向量)%

f(1) = 1;

f(2) = 2;

for k = 3:n

f(k)=f(k-1)+f(k-2);

end

fibonacci(12)

ans =

1

2

3

5

8

13

21

34

55

89

144

233

生成第n个斐波那契数

function f = fibnum(n)

if n <= 1

f=1;

else

f= fibnum(n-1) + fibnum(n-2);

end

>>fibnum(12)

ans =

233

>> n=40;

>> f= fibonacci(40)   %注意这里不用；%

f =

1

2

3

5

8

13

21

34

55

89

144

233

377

610

987

1597

2584

4181

6765

10946

17711

28657

46368

75025

121393

196418

317811

514229

832040

1346269

2178309

3524578

5702887

9227465

14930352

24157817

39088169

63245986

102334155

165580141

>> f(2:n) ./ f(1:n-1)

ans =

2.0000

1.5000

1.6667

1.6000

1.6250

1.6154

1.6190

1.6176

1.6182

1.6180

1.6181

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

1.6180

>> phi=1.6180

phi =

1.6180

>> f(2:n) ./ f(1:n-1) - phi

ans =

0.3820

-0.1180

0.0487

-0.0180

0.0070

-0.0026

0.0010

-0.0004

0.0002

-0.0000

0.0001

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

>> format long e

>> n = (1:40)';

>> f = (phi.^(n+1) - (1-phi).^(n+1))/(2*phi-1)    %.^代表的是数组幂%

%没有使用 ./ 是因为 (2*phi-1) 是标量，当除数为标量时，数组 ./ 的作用和矩阵右除 / 一样%

f =

1.000000000000000e+00

1.999924000000001e+00

2.999848000000001e+00

4.999620005776002e+00

7.999240017328002e+00

1.299848005198357e+01

2.099711212707026e+01

3.399460429456987e+01

5.499012064111847e+01

8.898214134576197e+01

1.439680827377117e+02

2.329434614407314e+02

3.769006026041551e+02

6.098263603418171e+02

9.866983185001744e+02

1.596478332038606e+03

2.583101661466575e+03

4.179458661151946e+03

6.762364006892249e+03

1.094150502918595e+04

1.770335509641367e+04

2.864402857121741e+04

4.634603821264375e+04

7.498788983768976e+04

1.213304057514294e+05

1.963125965094915e+05

3.176337811500838e+05

5.139314579022405e+05

8.315410988849569e+05

1.345433497996397e+06

2.176911399757839e+06

3.522242644808389e+06

5.698988599299847e+06

9.220963553667231e+06

1.491951902983353e+07

2.413978179027069e+07

3.905816693665795e+07

6.319611410351259e+07

1.022513126194834e+08

1.654426238183241e+08

>> f = round(f)

f =

1

2

3

5

8

13

21

34

55

89

144

233

377

610

987

1596

2583

4179

6762

10942

17703

28644

46346

74988

121330

196313

317634

513931

831541

1345433

2176911

3522243

5698989

9220964

14919519

24139782

39058167

63196114

102251313

165442624

实现分形蕨

function fern

%FERN 分形蕨的MATLAB 实现

%不会自动停止

shg   %显示图形窗%

clf reset

set(gcf,'color','white','menubar','none',...'numbertitle','off','name','Fractal Fern')

x=[.5;.5];   %起点坐标%

h = plot(x(1),x(2),'.');

darkgreen = [0 2/3 0];   %采用RGB三元组定义颜色%

set(h,'markersize',1,'color',darkgreen,'erasemode','none');

axis([-3 3 0 10])

axis off

stop = uicontrol('style','toggle','string','stop',...'background','white');   %在图形左下角标示stop键%

drawnow

p = [.85 .92 .99 1.00];

A1 = [ .85 .04; -.04 .85]; b1 = [0; 1.6];   %定义四个反射变量%

A2 = [ .20 -.26; .23 .22]; b2 = [0; 1.6];

A3 =[-.15 .28; .26 .24]; b3 = [0; .44];

A4 = [ 0 0; 0 .16];

cnt = 1;    %初始化绘图点%

tic        %开启秒表计时器%

while ~get(stop,'value')

r = rand;

if r < p(1)

x = A1*x + b1;

eleseif r < p(3)

x = A3*x + b3;

else

x = A4*x;

end

set(h,'xdata',x(1),'ydata',x(2));

cnt = cnt +1;   %使计数器加一%

drawnow

end

t = toc;   %记录时间%

s = sprintf('%8.0f points in %6.3f seconds',cnt,t);

text(-1.5,-0.5,s,'forntweight','bold');

set(stop,'stytle','pushbutton','string','close',...'callback','close(gcf)')