Recently I saw an interesting Earth Venus cosmic dance video on Facebook. See the original video below or here.
Although this is not entirely accurate from physics & astronomy perspectives, the dance is a stunning example of patterns that are generated by simple things.
I wanted to recreate this cosmic dance in Excel. How else am I to get my spreadsheet fix on a Saturday?
Here is a quick demo of the final outcome. Read on to learn more about the Earth Venus cosmic dance.
The details & assumptions
To create this cosmic dance, we need a few details
- Distance from Sun to Venus & Earth – 67.2 and 93 million KM respectively
- Number of days it takes to rotate around the sun – 224.7 and 365.25 respectively
We will also assume these incorrect things to keep our model simple
- Orbits of Earth & Venus are circular with Sun at center: In reality, they are elliptical, but as these are just stretched circles, we can assume circular orbits to keep the math simple.
- Sun is static: In reality, Sun (and entire solar system) is also moving. This means, this cosmic dance may never occur.
We also need one critical detail to graph this cosmic dance:
- The angular interval for plotting the lines. In the above examples, I have used 10° (ie there will be 36 lines around the circle). This is denoted by named range m in the model. You can adjust this in the output worksheet using a form control. Different values of m yield different patterns (although most of them will be pentagonal).
The math:
Generating planetary co-ordinates:
In a table, we will generate the positions (X & Y co-ordinates) of both Venus & Earth for 3000 points in time, each incremented by m degrees, starting at 0°.
To generate the X & Y values, we will use the x=r.cos? and y=r.sin? equations (where r is the distance from Sun and ? is the angle).
Drawing the lines:
This is the tricky part. At each step in the animation our line should from one tooth of the saw tooth pattern. See this demo to understand.
For more about this technique read – interactive network chart to map relationships between people.
So during each step of the animation, we add more co-ordinates to the chart (scatter plot) to generate this saw tooth pattern. Over time, this will yield the beautiful pentagonal cosmic dance.
We can generate these successive Venus & Earth co-ordinates from the calculations performed earlier by using MOD & INDEX formulas.
Once such saw tooth line data is generated, we will designate a cell to hold current animation position. Let’s call this pos.
We will then create two named formulas – dance.x and dance.y. These will contain the data necessary for our scatter plot. We will use OFFSET formula to generate these dynamic named formulas.
The chart
Now that all the necessary calculations are done, create a scatter plot with the dance co-ordinates. Set up X & Y axis minimum and maximum values accordingly (-160 to 160 should do). This ensures that the chart remains same no matter what step of animation we are on.
Also, add 3 more series to the chart
- One for a dot to represent Venus at current position
- One for a dot to represent Earth at current position
- One for a line connecting Venus to Earth
The animation
Next, let’s add a small macro to animate the chart. This macro will increment pos from 1 to a large number. After each iteration, we will call DoEvents so Excel can re-draw the chart. That is all.
Download the Earth Venus dance workbook
Click here to download the Earth Venus cosmic dance workbook. Enable macros to enjoy the dance. Play with form control to adjust the animation speed and pattern. Examine the data tab to learn more about the calculations.
Did you enjoy the dance?
I really liked the original video on FB and that is why I recreated this in Excel. This is a great exercise to show the power of simple things generating extraordinary patterns.
What about you? Do you like this Earth Venus dance?
More Excel animation and fun:
If you like animating things, you are going to love these tutorials. Check out,
24 Responses
I’d suggest simply using the subtotal function and filtering the data using the Win/Loss column. You get the same results and the formula is more comprehensible.
@John
That is one option.
There are times however when you want to see the whole data table or a filtered subset and still want to produce summary reports against an unfiltered field.
Is there a particular reason why you are using a comma and the unary (–) operator for the second array in the SUMPRODUCT formula? It seems to work the same if you were to string the arrays together using the asterisk (*). The advantage is that SUMPRODUCT treats the entire string of arrays as a single array.
@Mathew
Your correct, There is no difference.
I thought it may have been easier to explain this method.
Is there a way to do this on a large set of data? As in ~100,000 rows? When I try I get an error because the formula becomes too long. It says the max length of a formula is 8,192 characters. Excel 2010.
How do I incorporate a specific text within a cell for the second array. For instance, – -(C7:C13=”Apple”)
when I chose a specific text the formula does not work.
@RB
I am not sure what is the issue as if I use the sample data in the post the following work fine
Count:
=SUMPRODUCT(SUBTOTAL(3,OFFSET(C7:C13,ROW(C7:C13)-MIN(ROW(C7:C13)),,1)), –(C7:C13=”L”))
Sum:
=SUMPRODUCT(SUBTOTAL(3,OFFSET(C7:C13,ROW(C7:C13)-MIN(ROW(C7:C13)),,1)),(C7:C13=”L”)*(D7:D13))
You may want to check that there are no leading or trailing spaces in your list of Apples
I should have given a better explanation. Heres my situation. I have a column with cells filled with names like Column 1, Column 2, Pier 1, Pier 2, etc. If the cell just contained Pier and searched for that it works. But because it has other characters in the cell its not recognizing the pier. So how can I extract specific characters of a string of text in this formula?
Hopefully this was a better explanation
Hello-
This formula works pretty well for me except that it slow down excel and prevents some of my macros from working. I was wondering if there was a way to program this in VBA so that excel isn’t always trying to recalculate it. I would like to use a push of a button to get it to run then paste in a cell.
Thanks!
I am trying to sum filtered data in a column, but would want to ignore the negative values in the column. How to go about doing this?
@Akshay
Why not just add a filter to that column to only show the values greater than zero?
The negative values are required for reporting purposes, but their effect on the total is distorting the required output. Please advise.
@Akshay
I’d suggest making a post in the Chandoo.org Forums
http://forum.chandoo.org/
Attach a sample file to simplify the task
I have this working for counting and summing, however, I have a list and for the second array, I need a criteria. That is, I’m looking for b13:b200=”01.??.??” or =left((a1,2) or something like that. These types of criteria matches do not appear to work as I get a blank as a result.
Thanks!
@Bob
As your formula b13:b200=”01.??.??” looks like you are trying to check the first day of the month of the range
What about trying Day(B13:B200)=1
Hai Experts,
i understood this formula well and working fine in MS Excel 2013
but when the same am trying to place in google Spreadsheet it shows error as
“SUMPRODUCT has mismatched range sizes. Expected row count: 1. column count: 1. Actual row count: 2014, column count: 1.” and as a result #VALUE! Appears in cell.
Can anyone please help me how would i get it done in Google Spread sheet
or is there any other formula as a substitute for this.
Thank you very much.
thanks for providing this.. but why does excel keeps on prompting Circular referencing in cell D3?
@Vivek
I don’t know
I just downloaded the file and it is working fine and not showing that error
Goto the Formulas, Calculation Options Tab and check that Calculation is set to Automatic
What version of Excel and Windows are you using ?
I know that this forum is for MS Excel, but I am trying to help someone who is working in Google Sheets. The below formula works in Excel but Google Sheets returns:
“SUMPRODUCT has mismatched range sizes. Expected row count: 1. column count: 1. Actual row count: 39000, column count: 1.” and as a result #VALUE! Appears in cell.
This is the same problem asked by Srichirin above. Does anyone know if there is a formula for Google Sheets that will replicate what MS Excel does?
=SUMPRODUCT(SUBTOTAL(3,OFFSET($C$6:$C$39500,ROW($C$6:$C$39500)-MIN(ROW($C$6:$C$39500)),,1)),- -($C$6:$C$39500=H1),($D$6:$D$39500))
Trying to find a SUMPRODUCT formula that counts the word Closed by date for the last 7 days in a filtered list.
=COUNTIF(M:M,”>”&TODAY()-7) works ok for unfiltered count Column M contains Closure dates (blank if open) and Column L is Status Open or Closed
@ Terry
Please ask the question at the Chandoo.org Forums
https://chandoo.org/forum/
Please attach a sample file to ensure a quicker more accurate answer
I used this formula and worked like a charm! But, now I’ve been requested to use it but adding not one but two criteria in the same formula. For instance the sum I was doing added negative and positive numbers. I’ve been asked to use the exact same formula but adding that only positive numbers were considered… any idea on how to do this?
How exactly do you do sum filtered cells when two criteria are need not just one?
Thank you so much brother literally I have been struggling since morning to get the sum of the filtered category, however, after reading your blog attentively i got my solution, so thanks a lot once again.