Basic Examples

Subdivide the range 10–10000 in 3 steps:
[◼]
PowerSubdivide
[10,10000,3]
In[]:=
{10,100,1000,10000}
Out[]=

Scope

With two arguments, the start of the sequence is assumed to be 1:
[◼]
PowerSubdivide
[1000,10]
In[]:=
1,10
3/10
,10
3/5
,10
9/10
,1010
1/5
,10
10
,1010
4/5
,10010
1/10
,10010
2/5
,10010
7/10
,1000
Out[]=
PowerSubdivide can also perform on symbolic entries:
[◼]
PowerSubdivide
[a,b,4]
In[]:=
a,a
3/4
b
1/4
,
a
b
,a
1/4
b
3/4
,b
Out[]=
x
min
can be larger than
x
max
:
[◼]
PowerSubdivide
[1000,10,4]
In[]:=
1000,100
10
,100,10
10
,10
Out[]=

Applications

Choose point logarithmically useful for plotting on a logarithmic scale:
ListLogLogPlotTable{x,x^2},x,
[◼]
PowerSubdivide
[10,10^6,40]
In[]:=
Out[]=

Properties and Relations

The ratio between subsequent values is constant:
Ratios
[◼]
PowerSubdivide
[a,b,8]
In[]:=

b
1/8
a
1/8
,
b
1/8
a
1/8
,
b
1/8
a
1/8
,
b
1/8
a
1/8
,
b
1/8
a
1/8
,
b
1/8
a
1/8
,
b
1/8
a
1/8
,
b
1/8
a
1/8

Out[]=
PowerSubdivide
is related to
Subdivide
:
[◼]
PowerSubdivide
[10,20,8]==Exp[Subdivide[Log[10],Log[20],8]]
In[]:=
True
Out[]=
Negative and positive end points results in intermediate values in the complex plane:
ComplexListPlot
[◼]
PowerSubdivide
[-10,25,40]
In[]:=
Out[]=
Calculate the geometric mean of two values:
[◼]
PowerSubdivide
[6.0,10.0,2][[2]]
In[]:=
7.74597
Out[]=
Compare to the built-in function:
GeometricMean[{6.0,10.0}]
In[]:=
7.74597
Out[]=

Possible Issues

If the start or end is a negative number, intermediate values might be complex numbers:
[◼]
PowerSubdivide
[-1.0,1.0,10]
In[]:=
-1.+1.22465×10
-16
,-0.951057+0.309017,-0.809017+0.587785,-0.587785+0.809017,-0.309017+0.951057,6.12323×10
-17
+1.,0.309017+0.951057,0.587785+0.809017,0.809017+0.587785,0.951057+0.309017,1.
Out[]=
If both end points are negative real numbers
Chop
might be needed to remove approximate zeros:
values=
[◼]
PowerSubdivide
[-1.0,-100.0,10]
In[]:=

Neat Examples

Connect pairs of random complex numbers: