Few days ago, I saw a beautiful homemade science experiment on Sand Pendulums on Bruce Yeany’s YouTube channel. Go ahead and check it out. It is a cool project to do with your kids.
I will try this experiment with kids during school term holidays around Easter. But first, I wanted to try the simulation in Excel.
Simulating sand pendulum pattern in Excel
Take a look at the final simulation.
Pendulum pattern – Lissajous curve
The patterns generated by sand pendulum are nothing but Lissajous curves. We can generate these curves in Excel by using below equations.
- X = A * SIN(a*t + d)
- Y = B * SIN(b*t)
where
- A & B refer to amplitude (the length pendulum travels before reversing its direction) along X & Y axes
- a & b refer to height of pendulum along X & Y axes (if these are same you get a simple pendulum and thus a straight line pattern)
- d refers to degrees of shift (its a bit complex to explain here, but read about phase shift on Lissajous curve Wikipedia page)
- t refers to radians (degrees).
But this will generate a smooth line, how to show sand?
Simple, after computing each pair of (X, Y) we add a small random noise to them. This creates an impression of sand falling from pendulum on to a surface and bouncing off. Let’s define our new equations as,
- X = A * SIN(a*t + d) + jx * rand()
- Y = B * SIN(b*t) + jy *rand()
Where jx & jy are jitter fractions (very small numbers, lest the dots will be too away from original points)
What if the pendulum never stops?
Since we are simulating the movement of a pendulum in Excel, we can choose to have a never stopping pendulum (ie a simple gravity pendulum). In this case A & B values never change.
In real life, A&B will reduce with each oscillation until the pendulum comes to a stop (because there is air drag, friction and other forces at play too).
Let’s look at the chart & VBA
Enough physics & maths. Let’s take a look at the chart & VBA behind this simulation.
- Set up 3 columns, one with t values starting from 0 and increasing by 0.05 per cell, next two with X & Y values.
- Leave the X&Y values blank. We will use VBA to fill these.
- Let’s say we use 5000 (x,y) values to plot the chart. This gives enough variation. You can alter the number of rows later.
- Create a scatter plot with smoothed line using these 5000 (x,y) values.
- Using VBA, iterate thru column t and calculate X & Y values for each t value using above equations.
- Update the chart by using doEvents after every n calculations. Try n=25 first and change as you see fit. Updating the chart after every calculation slows down the animation significantly.
- Change A, B, a, b, d, jx, jy and air drag factors to generate different curves.
Here is the VBA code used for the animation.
Sub animate()
Dim xVal As Double, yVal As Double, jx As Single, jy As Single
Dim t As Range
Dim a1 As Single, drag As Single
Dim a2 As Double, b2 As Double, d As Double
Dim updateScreen As Integer
Dim tVals As Range
a1 = 1
drag = Range("air.drag")
a2 = [a.2]
b2 = [b.2]
jx = [j.x]
jy = [j.y]
d = WorksheetFunction.pi() / Range("d")
Set tVals = Range("t.vals")
Range(tVals.Offset(, 1), tVals.Offset(, 2)).ClearContents
Range("done") = "drawing..."
For Each t In tVals
xVal = a1 * Sin(t * a2 + d) + jx * Rnd()
yVal = a1 * Sin(t * b2) + jy * Rnd()
t.Offset(, 1).Value = xVal
t.Offset(, 2).Value = yVal
'update screen after every 25 times this loop has run
updateScreen = IIf(updateScreen = 25, 0, updateScreen + 1)
If updateScreen = 0 Then DoEvents
'Reduce A & B values by using drag
a1 = a1 * (1 - drag)
Next t
Range("done") = "done"
End Sub
Download Pendulum Sand Patterns Workbook
Click here to download the Pendulum Sand patterns workbook. Play with the animate & random pattern buttons to see some cool patterns.
Have you done this experiment?
This is a cool way to teach kids the awesome pattern power of simple things in life. Have you done this experiment? If not, give it a try. If you think playing with sand is too messy, try the Excel workbook.
Also check out: 3D dancing pendulums post to see some cool & clever animations. Huge collection of spreadsheet tools & simulations for teachers.
30 Responses to “Rescue oddly shaped data – Battle between Formulas, VBA and Power Query”
Nice use of Power Query! Power Query is simply awesome! But somehow a lot of people are punishing themselves by not using it (not learning it).
An imperfect 4th approach for consideration... no codes at all...
Select myrange.
Go to Special --> Blank
Delete Cell --> Shift cell left
90% done... now we just need to move the data of 2nd column to the bottom of 1st column
Of course... Power Query is the best.
Cheers,
There is another way but it involves multiple steps:
Copy the values in column E, move the cursor to F5, Paste Special with Skip Blanks, OK
Copy the values in column D, move the cursor to F8, Paste Special with Skip Blanks, OK
And so on.
This works perfectly, albeit a little clumsily apart from the values in B17 and C16, which can be moved with simple copy and paste
Power Query Forever! I do not know how I survived for so long without knowing and using this tool, I can not recommend it to my colleagues, but by the way they prefer to suffer to learn.
My congratulations here from Brazil.
I rolled my eyes when I saw that data
Using decimal places is a nice trick to order data, thanks for that
And tweaking the first formula a bit, you can use OFFSET instead of INDIRECT
=OFFSET($A$1, MIN(IF(myrange, ROW(myrange)), ROWS(A$1:A1))-1, RIGHT(TEXT(MIN(IF(myrange, ROW(myrange) + COLUMN(myrange)*0.00001), ROWS(A$1:A1)), ".00000"), 5)-1)
Tried the above formula with the downloaded oddly shaped data file and I could not get it to work. I get #value without ctrl+shift+enter, and #ref with ctrl+shift+enter.
Sorry, it was SMALL, not MIN.
Add with CTRL+SHIFT+ENTER.
Thank you for your formula. Like the indirect formula I tested this one in older versions of EXCEL and it worked without ALTERATION in EXCEL 95. Very impressive.
Too complicated
Use =Sum to summarize all the sells to the left and Bobs Your Uncle
@Bertie... I am afraid that won't work when you have more than one value in a row.
I tested this formula in versions of Excel all the way back to Excel 95
=IF(ISERROR(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(MyRange"",ROW(MyRange)+COLUMN(MyRange)*0.00001),ROWS(A$1:A9)),"00000.00000"),".","C"),FALSE)),"",(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(MyRange"",ROW(MyRange)+COLUMN(MyRange)*0.00001),ROWS(A$1:A9)),"00000.00000"),".","C"),FALSE)))
So there are multiple ways of cleaning up messy data by formulas.
Wow.. Excel 95. Who knew people still use that. But as you have shown, Excel has all these beautiful and powerful functions for 23 years. It has data sciency stuff before DS was even a thing.
I had a problem with pasting the formula in the original post.
Formula should be: =IF(ISERROR(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(myrange"",ROW(myrange)+COLUMN(myrange)*0.00001),ROWS(A$1:A1)),"00000.00000"),".","C"),FALSE)),"",(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(myrange"",ROW(myrange)+COLUMN(myrange)*0.00001),ROWS(A$1:A1)),"00000.00000"),".","C"),FALSE)))
EXCEL even in a 16 bit version, is a very robust and capable program.
I don't like the VBA code. If you have a blank row in MyRange, the last entry in the range is doubled up in the paste.here range.
Not really. The macro is writing one cell at a time from paste.here. You have to clean the range before, which I was too lazy to write. But a line like Range(range("paste.here"), range("paste.here").end(xldown)).clearcontents should do the trick.
Adding Range(range("paste.here"), range("paste.here").end(xldown)).clearcontents fixed the problem.
for step split column by delimiter i am not getting option of split into rows or columns. Can you help me in this
Thanks Chandoo for promoting Power Query.
To simplify further, you can "Unpivot Columns" instead of right click on the newly created column and split it by comma in to rows in step 3 of Power Query.
i used
=LOOKUP(10000,B5:F5)
and got the answers. I just plagiarized this formula somewhere and use it, maybe you can explain why it works.
Regards
@Johan... I am not sure if the formula works correctly. When I tested it with the sample data in this post, it showed #N/As in two cells. Essentially, it will only give first value in each row. So if a row has multiple values, then subsequent values are missed. LOOKUP() function goes thru a list and finds the first value that is less than or equal to the input - in this case 10000 in B5:F5.
I have the need to convert pdf's to excel on occasion and they often come out a mess like this. I have used:
Cell G2 =COUNT(myrange)
Cell G3 =IFERROR(IF(G2-1<1,"",G2-1),"") copied down to G100
Cell H2 =IFERROR(LARGE(myrange,G2),"") copied down to H100
Waouw...
=IFERROR(INDIRECT("R" & SUBSTITUTE(TEXT(SMALL(IF(myrange "", ROW(myrange) + COLUMN(myrange)*0.00001),
ROWS(A$1:A1)), "00000.00000"), ".", "C"), FALSE), "")
but CTRL Shift Enter with {} before and after 🙂 😀
Here's a way with pivot table
https://www.bookkempt.com/2018/02/aligning-non-contiguous-data.html
This is brilliant. Bookmarked 🙂
Another possibility.
This assumes that you have a row index 'k' to use in the SMALL function and a column index 'h' to identify the columns of 'myRange'.
If you define 'coord' to refer to
=k+h/10 [assuming h<10]
then it will be possible to recover values later based upon location within 'myRange'. The formula 'nb' that identifies non-blanks by coordinates is given by
= SMALL( IF(myRange"", coord), k )
Finally, to unpick the pieces
= INDEX( myRange, INT(nb), 10*MOD(nb, 1) )
Whilst I am here and making trouble the PQ solution is also a tad over-complicated. All that is needed is to unpivot the entire table and remove the Attribute column.
The advanced editor would show
let
Source = Excel.CurrentWorkbook(){[Name="myRange"]}[Content],
#"Unpivoted Columns" = Table.UnpivotOtherColumns(Source, {}, "Attribute", "Value"),
#"Removed Columns" = Table.RemoveColumns(#"Unpivoted Columns",{"Attribute"})
in
#"Removed Columns"
1.fill the blank cells with 0
2.the requested column value=sum of those mess number column
but this can be used in only one column has value
Chandoo
And if we use the formula SEARCH (100000000, B5: F5)
JC
Another approach with Power Query, it will still work if the number of columns changed:
let
Source = Excel.CurrentWorkbook(){[Name="myrange"]}[Content],
#"Added Custom" = Table.AddColumn(Source, "List", each Record.ToList(_)),
#"Removed Other Columns" = Table.SelectColumns(#"Added Custom",{"List"}),
#"Expanded LIst" = Table.ExpandListColumn(#"Removed Other Columns", "List"),
#"Filtered Rows" = Table.SelectRows(#"Expanded LIst", each ([List] null))
in
#"Filtered Rows"
Cool idea to use Record.ToList as added column. Thanks for sharing this.
Nowadays, you can just use TOCOL on Excel 2024, MS 365, and Web Excel. It has a parameter to ignore blanks/errors/both.