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.
39 Responses to “Some charts try to make you an April fool all the time (or why 3d pie charts are evil)”
Another little trick they've used in that pie chart is in the positioning of the car sales in relation to each other. The way in which you present them in the column chart is from highest seller to lowest seller, left to right, which is what we're used to seeing. But in the dastardly pie chart, the two smallest selling cars (the SX4 and the Scala) are placed one either side of the Verna, which serves to make it look bigger again.
Also the perspective at which you look at the pie chart makes the Verna look bigger. From my experimintation, a perspective of around 35-37 degrees makes it look like an even bigger slice, which appears to be what the advertiser has done.
All of this manipulation would make you think of the "photoshopping" or "air-brushing" that is done on photos of models, film stars, and so on, in magazines, to give them the unattainable looks, skin, shape, etc., etc., that many aspire to, but can never reach.
This post is quite the learning experience, thanks very much.
please help!!!! im taking a computer class at SPC in clearwater. i have an excel worksheet to turn in and my pie charts are just blank no pie at all, all the other charts are working but i need #D pie chart can anyone help me to restore the 3D Pie chart??? Emergency
@Amanda
Select the Chart
Right Click it
Change Chart Type
Select a 3D Pie chart type
This is a great example of why I do not like pie charts.
I promise to never make a 3d pie chart. If I ever see one, I promise to not rotate or explode it. I also promise to create alternative charts (usually column, bar, line or scatter plots) so that my audience can see the truth better.
And oh yeah, I promise to bake & eat pies whenever possible. Apart from cakes, pastries, ice creams, biscuits and other assorted fun foods that is.
signed David Onder
Reminds me of the quote ... statistics are like bikinis ... what they reveal is suggestive, what they conceal is vital.
I love that Quote and you are so right, now to get the upper management to understand that!!!
Oh .. and wont it be awesome if u can create a quick decision tree tool for jo so that she can buy shoes :p ... perhaps link it to jabong.com or flipkart.com account and boom ... a spreadsheet shopping tool!
There are a only two acceptable pie charts: actual pie and cheesecake.
My own commitment to the truth is to incorporate pereto graphs (Few, 2006) into most of my bar/column graphs. The pereto is activated by a non-printing check box form control. This method has proven its worth on a number of occasions when presenting data and demonstrating its integrity when challenged - Also gets a kudos point from the boss for foresight, preparedness and professionalism :-).
Leonk
Hi Leon,
Can you elaborate? I'm aware of pareto as the 80/20 rule what do you mean by you "include" it?
@JungleJme
A Pareto Chart is a Ranked Column chart
With the column of the highest Rank occurring at the left and the Smallest column at the right
It highlights the issues with most impact easily
Have a read of: http://chandoo.org/wp/2009/09/02/pareto-charts/
A little part of me dies inside whenever I see presentations from upper level technical management that includes exploded 3D pie charts.
I promise to never make a 3d pie chart. If I ever see one, I promise to not rotate or explode it. I also promise to create alternative charts (usually column, bar, line or scatter plots) so that my audience can see the truth better.And oh yeah, I promise to bake & eat pies whenever possible. Apart from cakes, pastries, ice creams, biscuits and other assorted fun foods that is.signed Luke M
So if the goal is to mislead, 3-D pie charts are great. There is a use for everything.
Definitely agree with you. They did the appropriate thing as a marketing scheme. The chart is not "wrong" in any way, just misleading to the eye.
I think it's an excellent ploy.
I think these are an excellent display of the versatility of storytelling that is allowed by the champion of charts, the pie. Great work Chandoo. See my site for some further examples of effectively working with pie charts. eagerpies.com
Well done Chandoo, all points clearly made; I'd add that there are lies, damned lies, statistics, pie charts and tweaked pie charts.
I never recommend a pie chart but some of my custoners are so stupi are sure their requirements are correct. And the customer is always right (when he is the boss). So no pledge but lots of support.
When I teach charts I ask what is the purpose of charts? Fairly sharp students talk about information over data. The purpose is to make better decisions happen. The accuracy is essential, the usability is essential, but the real gain is when the manager sees what to do to make the figures better.
Why do you have strikethru option in replies that is visble when editing but lost when posted? Of course is this does show a strikethru I must have got it wrong; let's see..
... no thought not. Register aplea for strikethru to work. Thanks
Hand on experience, thank you for sharing this.
My favourite (if that's the right word) is Stve Jobs at
http://www.myspace.com/crazyalaskandude/photos/30206354
Some people must be assumed to know better, in which case it must be intentional.
There's a classic book called How to Lie with Statistics, and another called How to Lie with Maps. Time for How to Lie with Charts?
A time and a place for everything, in my opinion. E.g. pie charts are good for communicating specific things to a wide and general audience, because everyone feels comfortable with the form at least.
3D pie charts are good for giving the appearance of analysis to people who wouldn't read them anyway.
In Excel, I use flattened 3D pie charts because they let me control the rotation of the chart to put the most important slices where I want them. That said, I don't use pie charts very often because my audience doesn't demand them
Sorry, but all kind of 3d stuff is horrible! Better, let's back a pie!
Sorry, but all kind of 3d chart stuff is horrible! Better, let's back a pie!
Ha Ha you are right, but why 3D on a flat screen that doesn't work I think and in the end it's all about the data right..
Call this the chandoo effect!!! Did u check out the same advertisement with a different type of chart in yesterdays newspapers??? Even the marketing managers listen to chandoo.
I've always disliked pie charts for this reason and exploded 3d pie charts makes a liar out of their creators. its like the old man and his fish story.... I promise to never make a 3d pie chart (unless its as a joke). If I ever see one, I promise to not rotate or explode it. I also promise to create alternative charts (usually column, bar, line or scatter plots) so that my audience can see the truth better.
And oh yeah, I promise to bake & eat pies whenever possible. Apart from cakes, pastries, ice creams, biscuits and other assorted fun foods that is.
I teach mathematics at high school, and this article will now feature as a regular teaching tool in the topic Misleading Graphs. Thank you.
...and along those lines, I realise I need to create more exploded 3D pie charts, more over-formatted graphs and more line graphs for categorical data to demonstrate poor graph choice.
...and the staircase graph is even worse than the 3D pie chart. When you analyse it in terms of the amount of yellow on the graph compared to any other colour - particularly green which was second - it appears that Verna holds at least 50% market share.
I ran through this graph as a lesson on Misuse of Graphs. We placed a 5mm grid over the image of the graph and counted the squares. The image is 58% yellow. This surprised the students because they were analysing the chart and interpreting it as about 40%. I remarked that the 58% yellow was influencing their judgement. It was a very good lesson.
Thanks for this great teaching resource.
For most practical reasons, I believe there is no need to use a 3D chart unless a Z-axis is needed for your data -- and pie charts need not be 3D since they don't need to show any axis!
Your method of telling the whole thing in this paragraph is genuinely good, every one be capable of simply
understand it, Thanks a lot.
I agree about pie charts. I didn't recognize the name "Verna" so I had to Google it: Hyundai sells the same car in the US as the "Accent."
I cant stand 3d pie charts. 2d ones are bad enough. And im my opinion the staircase chart is even worse. Note that with the verna we see two sides which gives it a visible width on the page/screen about three times as wide as the second highest scoring one, where we can only see one side of it.
However, I won't make the promise. Whilst I think acurate representation of stats is a morale obligation of those who need to present impartial data, you have to admire the marketing team for not missing a single trick.
Unfortunately with slick charts with the lighting and 3d effects, it makes acurate flat charts look boring and unprofessional to the uniformed 90% who view style over substance.
As an example of this, I was reading information packs from vendors, and out of the dozen or so, not a single one had flat charts....
Hi, Chandoo!
Can we download some chart template like in your post? ))
It is really pretty.
[…] Ah good day to my Tableau disciples. Peace be with you. May your day be free of exploding 3D pie charts… […]
[…] ovšem uvádí Chandoo, kolá?ové grafy lze naproti tomu dob?e využít k manipulaci. Linkovaný p?íklad s videem […]
[…] Even people who have the best of intentions create graphics that mislead just because they don’t know about statistics, they don’t know about logic, they about the principles of visualization. It’s not their fault, just like it was not my fault 10 or 15 years ago. Nobody had educated me. It was only through the process of reading books, studying, and learning from other people that I discovered the many mistakes that I’d made in the past, for example, creating 3D pie charts. […]
I think if the point is to create BS, everything should be not only in 3d but in 4d!
4d FTW
[…] makes it very difficult to visually compare data. A good example of how misleading a 3-D charts can be found here. Less is more. Make your visualizations as simple and clean as possible, it makes them much easier […]