Motion Induced Blindness

Hello All.

My name is Ian Huitson “Hui“.

I am quite honored that Daniel has invited me to become a regular contributor here at the Excelhero.com/Blog and hope I can maintain the high standard on content that this site has become renowned for. I look forward to your feedback on this and future posts.

A few months ago I spotted a new optical illusion over at http://www.michaelbach.de/ot/mot_mib/index.html

I figured I’d give it a go in Excel and this post documents
my approach to a solution.

Motion Induced Blindness

What to see

On the right you see a rotating array of blue crosses and 3 yellow dots.
Now fixate on the centre (watch the flashing red/green spot). Note that the yellow
spots disappear once in a while: singly, in pairs or all three simultaneously, right?
In reality, the 3 yellow spots are continuously present, honest! This is captively called “motion induced blindness” or MIB.

What to see (copied from

Below you see a rotating array of blue crosses and 3 yellow dots. Now fixate on the centre (watch the flashing red/green spot). Note that the yellow spots disappear once in a while: singly, in pairs or all three simultaneously, right?

n reality, the 3 yellow spots are continuously present, honest! This is captively called “Motion Induced Blindness” or MIB.

What to see

On the right you see a rotating array of blue crosses and 3 yellow dots.
Now fixate on the centre (watch the flashing red/green spot). Note that the yellow
spots disappear once in a while: singly, in pairs or all three simultaneously, right?
In reality, the 3 yellow spots are continuously present, honest! This is captively called “motion induced blindness” or MIB.

The actual MIB Excel model is much smoother than this animated GIF representation.

The MIB Model

There were three approaches I thought about using for this optical illusion.

1.   Use a single series to define all the points
(49) and place a cross at each point.

2.   Use 2 series to define each cross, there are 49
crosses.

3.    Use a Bitmap for the Background including
crosses and rotate it.

Choice of Attack

The first method wouldn’t suit the needs of the illusion as each
marker doesn’t rotate as the series is rotated, but instead stays fixed
relative to the ordinal axis.

The second method would require a large number of
co-ordinates for each cross, that is 4 X and 4 Y co-ordinates for each cross
and there are 49 Crosses, for a total of 98 series, and 196 co-ordinates. Time
consuming but at least the crosses will rotate. This is the methodology I choose for the model.

The Third method of rotating a fixed bitmap although very
feasible, wasn’t I felt in the spirit of doing it all in an Excel Chart. I
should note that this method would allow for much faster rotation than has been
achieved using Method 2.

You can follow along with the real model and all associated preparatory workings in the attached file: Motion Induced Blindness.xlsm. All preparatory workings described below are on worksheet “2”.

Setup

Firstly I setup a table of numbers -3 to +3 in X and Y and
then added/subtracted a small amount to each one to represent the width of the
cross. I settled on 0.15 as it looks about right.

This gave me a table of X and Y values for each point.

 Offset 0.15 Pt No X1 X2 Y Circle Quadrant 1 -3.15 -2.85 -3 3 2 -2.15 -1.85 -3 3 3 -1.15 -0.85 -3 3 4 -0.15 0.15 -3 3 5 0.85 1.15 -3 4 6 1.85 2.15 -3 4 7 2.85 3.15 -3 4 8 -3.15 -2.85 -2 3 9 -2.15 -1.85 -2 3 10 -1.15 -0.85 -2 3 etc

Rotation

The problem with X and Y values is that to rotate them
around a point it is easier to use Polar coordinates, but Excel requires
Cartesian Coordinates to plot.

So the process would be

1.
Setup the 49 points of 4 sets of X, Y pairs

2.
Transform them to polar co-ordinates.

3.
Setup a named formula for each end point

4.
coordinates

5.
Use a named formula to convert the polar
coordinates to Cartesian coordinates

6.
Plot

7.
Repeat from Pt 4.

Polar Co-ordinates

Point 2 in the above sequence means converting each set of
coordinates into polar co-ordinates consisting of Radius r and Angle Ø.

Solving the above we have

r           =sqrt(x2
+ y2)

= Sqrt(-2.852 + -22)

Ø          = Atan(y/x)

=Atan(-2/-2.85)

This is done for every end point of each cross section, 98 pairs
of X, Y Co-ordinates.

Now we have the polar co-ordinates of the end points, we can
setup the rotation equations.

That is the equations to convert the original polar
co-ordinates back to X & Y values, which Excel needs to plot.

This is done by 2 simple equations:

X = r * Cos(Ø)

Y = r * Sin(Ø)

X = 3.731*cos(3.707)

Y = 3.731*sin(3.707)

Now we can add a rotation angle, lets
use t.

So that the new position after
rotation is

X = r * Cos(Ø + t )

Y = r * Sin(Ø + t )

Xrot = 3.731*cos(3.707 + t)

Yrot = 3.731*sin(3.707 + t)

This is done for each point of the
cross for all crosses.

 x1 y1 4.350*cos(3.903+t) 4.350*sin(3.903+t) 3.691*cos(4.091+t) 3.691*sin(4.091+t) 3.213*cos(4.346+t) 3.213*sin(4.346+t) 3.004*cos(4.662+t) 3.004*sin(4.662+t) 3.118*cos(4.988+t) 3.118*sin(4.988+t) 3.525*cos(5.265+t) 3.525*sin(5.265+t) 4.138*cos(5.472+t) 4.138*sin(5.472+t) 3.731*cos(3.707+t) 3.731*sin(3.707+t) 2.936*cos(3.891+t) 2.936*sin(3.891+t) 2.307*cos(4.191+t) 2.307*sin(4.191+t) etc.

Matrix Arithmetic

To draw a line on a scatter chart,
Excel needs 2 X values either in a Range or an Array as well as 2 Y values in a
Range or Array.

Thankfully I’ve been a member of
Daniel’s Excel Hero Academy. In a Module on Matrix Arithmetic we learn
that we can add 2 named formulas together to make an array in a Named Formula.

We need to do this to end up with an
Array representing the X and Y values for each of the 98 segments of the 49
Crosses.

X Values = { X1, X2 }

Y Values = { Y1, Y2 }

As an Excel Named Formula I used:

Named
Formula   Formula

sx_08                     =
{1,0} * 3.731*cos(3.707+t)  + {0,1} *
3.482*cos(3.753+t)

sy_08                     =
{1,0} * 3.731*sin(3.707+t)  + {0,1} *
3.482*sin(3.753+t)

This is done for all the 98 cross
segments.

To simplify the construction of all
these, the co-ordinates, transformation to polar coordinates and construction
of the rotated transform formulas was done in Excel (Refer Worksheet “2” in the
example file).

This allows errors in co-ordinates to
be checked.

Once all the named formula are ready to
be uploaded, I have used a technique involving a simple VBA Named Formula
upload subroutine. This is described in my post at:

The VBA routine is available in Module
2 of the attached Sample File, “Load_Named_Ranges()”.

Once the named formula are constructed
and loaded, it is simply a matter of adding a blank scatter chart to Excel and
setting up a table of Series Names, X value and Y Values:

 Chart Series Name X values Y values S01 =1!sx_01 =1!sy_01 S02 =1!sx_02 =1!sy_02 S03 =1!sx_03 =1!sy_03 S04 =1!sx_04 =1!sy_04 S05 =1!sx_05 =1!sy_05 S06 =1!sx_06 =1!sy_06 S07 =1!sx_07 =1!sy_07 S08 =1!sx_08 =1!sy_08 S09 =1!sx_09 =1!sy_09 S10 =1!sx_10 =1!sy_10 Etc

Once again I have setup a table of
Named Formula name, together with X and Y Named Formula and used a small VBA
routine to add these series to the chart.

The VBA routine to do this is available
in Module 2 of the attached Sample File, as “Add_Cht_Series()”.

The 3 Yellow Spots

The 3 yellow spots are a manually loaded
series in the chart using an Array of coordinates.

X Series                              ={1.5, 0, -1.5}

Y Series                              ={1.5, -1.8, 1.5}

The Marker was set to Yellow and size
15

The Line Type was set to None

The Centre Spot

The centre spot was a manually loaded
series in the chart

X Series                              =0

Y Series                              =0

The Marker was set to Red and size 12.

The Line Type was set to None.

Animation

Animation of the chart is achieved by
adding a simple Named Formula “t” and the changing the value of t and updating
the chart.

This is done through a simple VBA
routine “Rotate()”

This is described below

Sub Rotate()

Dim t As Double
‘Dimension
the only variable

t = 361 ‘Start at 361 Degrees

Do While [AA1]
‘Loop while cell AA1 is True

t = t – 1
‘Decrease
rotation angle by 1 Deg

If t = 0 Then t = 360
‘If Rotation
= 0 go back to 360

ActiveWorkbook.Names.Add Name:=”t”, RefersToR1C1:=(t * 2 * Pi
/ 360)

named Formula t with value = t * 2 * Pi / 360

DoEvents
‘Refresh
screen

If (t >= 0 And t < 90) Or (t >= 180 And t < 270) Then
‘If t in a range set Centre Marker color
Red or Green

ActiveSheet.ChartObjects(“Chart
2″).Chart.SeriesCollection(99).Format.Fill.ForeColor.RGB = RGB(255, 0, 0)

Else

ActiveSheet.ChartObjects(“Chart
2″).Chart.SeriesCollection(99).Format.Fill.ForeColor.RGB = RGB(0, 255, 0)

End If

Loop

End Sub

The above example is attached below:

Worksheet 1, contains the working model.

Worksheet 2, contains the original
source data as well as all transformations of it.

FINALLY

This is my second post at ExcelHero.com
and I’d like to thank Daniel for allowing me to
post here again.

I am a member of the inaugural Excel
Hero Academy and MVP of the Excel Hero Academy 2 & 3, where Daniel explains a lot of the techniques you will see throughout this site as well as so much more.

It is one of these techniques that made
this project possible.

I am a regular contributor at
Chandoo.org where I answer questions at the Forums and have contributed over 30 Posts.

Excel Optical Illusions Week #29

This week’s Excel Optical Illusion is called Kaleidoscope Motion and was originally created by Peter van der Helm in 2007. I modeled mine after Michael Bach’s version, but with a twist:

From Michael Bach’s site…

The red cogwheel rotates, but does it rotate smoothely? Physically, the rotation is perfectly smooth as you can confirm by making parts of the arrangement transparent. However it seemingly jolts ever so often.
To my eye it looks as if the blue inner cog jumps to the left periodically. While I included the outer cog, I decided to color it white to enhance the effect.
My Excel version of the illusion uses simple shapes that are grouped and rotated via VBA.
As always, the workbook animation is much, much better than the GIF.
Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero Newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)
– Freezing Rotation (Optical Illusion)
– Reverse Spoke Illusion (Optical Illusion)
– Stepping Feet Radial Illusion (Optical Illusion)
– Swimming Fish (Optical Illusion)

– Mutually Interfering Shapes (Optical Illusion)

– Kaleidoscope Motion (Optical Illusion)

Excel Optical Illusions Week #28

This week’s Excel Optical Illusion is called The Mutually Interfering Shapes Illusion and was originally created by Maarten Wijntjes, Robert Volcic and Tomas Knapen. The illusion was a 2008 Finalist in the Best Illusion of the Year Contest hosted by the Vision Sciences Society.
Here is how they described the illusion for the contest…

A circle’s a circle and a square’s a square, right? Wrong! Just look at the center of our MISillusion display and you’ll see why – Two dots are moving around bouncing off one another. Do you see a square and a circle? They really are! The illusion becomes even stronger when tracing the inner square closely: you’ll see the outer dot moving along four arcs instead of one circle. If you now follow the outer dot, the square suddenly seems curved inward!
So watch out next time you track a baseball pitch, your brain might just throw you a curveball!
My Excel version of this illusion is much smoother than the animated GIF above can reproduce. Wow that’s starting to sound like a broken record, but it’s the truth.
This is an XY Scatter chart with a little VBA for the animation. I’m very happy how it turned out, especially the color fading happening simultaneously with the rest of the animation. Again, the workbook is much, much better than the GIF.
Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero Newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)
– Freezing Rotation (Optical Illusion)
– Reverse Spoke Illusion (Optical Illusion)
– Stepping Feet Radial Illusion (Optical Illusion)
– Swimming Fish (Optical Illusion)

– Mutually Interfering Shapes (Optical Illusion)

Excel Optical Illusions Week #27

As promised last week, the Smith Chart will be published in a few hours. It is one of the most demanding charts I have ever created, and it is just about ready. Please look for it Monday.
In the meantime, this week’s Excel Optical Illusion is called Swimming Fish, and was originally created by Emily Knight and Arthur Shapiro. It was a 2007 Finalist in the Best Illusion of the Year Contest hosted by the Vision Sciences Society.
Are the fish bobbing up and down? I can assure you that they do not move.
My Excel version of this illusion is much smoother than the animated GIF above can reproduce. It includes an option to remove the moving background, which eliminates the illusion.
This is an XY Scatter chart with a little VBA for the animation. Pretty straightforward but I like how the background lines were made to seem infinite when there are only six of them in actual fact.
Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero Newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)
– Freezing Rotation (Optical Illusion)
– Reverse Spoke Illusion (Optical Illusion)
– Stepping Feet Radial Illusion (Optical Illusion)
– Swimming Fish (Optical Illusion)

Excel Optical Illusions Week #26

In a couple of days I will be starting a new series of high precision engineering charts, starting with the publication of the compelling Smith Chart.
In the meantime, this week’s Excel Optical Illusion is called the Café Wall Illusion.

Are the tiles and horizontal lines parallel?
The Excel version of this illusion was crafted by Excel Hero reader, Hui. Another fantastic job, Hui. I also received a version of the Café Wall from Tim McCollough, but I’ve lost it. Tim if you send it to me again, I’ll post it here!
Hui’s version is a 100% Stacked Bar chart. Very cool. It’s a dynamic chart with a slider control that allows you to adjust the tiles. When they are aligned vertically, the illusion disappears completely.
Here is the file.
— UPDATE —
Tim McCollough was kind enough to resend his version of the Café Wall Illusion – also a very fine implementation.
Here is Tim’s file:
If you like my blog, please be sure to sign-up for the new Excel Hero Newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:

Excel Optical Illusions Week #25

This week’s Excel Optical Illusion is called the Stepping Feet Radial Illusion.

As Michale Bach describes this illusion on his page that inspired me…
… Observe the move ment of blue and yellow patch es (‘feet’). Whenever the [radial] grid is visible, the feet seem to step out of phase, while in reality their movement is always par al­lel. Like tiny feet going tip-tap-tip-tap… The effect is more pronounced if one does not look directly on to the feet.
This project started out as a chart, but I was not happy with the outcome so I changed it to animated shapes. The spokes image in the background was creates with a Radar chart. I left the named formulas for the series in the name manager if you would like to look at them.
The “feet” are shapes grouped together with an invisible line that stretches all the way across the circle, centered on the circle’s center. For the animation I use VBA to rotate this grouped shape.
At every 12% of the way around the circle, the VBA toggles the visibility of the radial grid. When the grid is not visible it is obvious that the feet never shift but are locked in parallel motion.
Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)
– Freezing Rotation (Optical Illusion)
– Reverse Spoke Illusion (Optical Illusion)
– Stepping Feet Radial Illusion (Optical Illusion)

Excel Optical Illusions Week #24

This week’s Excel Optical Illusion is called the Reverse Spoke Illusion.

Which way are the spokes moving?
As Michale Bach describes this illusion in the his page that inspired me…
… The wheel defined by the dark-bright sectors is rotating clockwise and the spokes are rotating counter-clockwise?

Look again… The spokes stay put! Rather, each spoke makes a tiny shift in one direction and then slowly (subliminally) moves back.
I think this is the first time in ten years I’ve used a pie chart! This illusion uses VBA code very similar to butterfly rainbow to vary the colors of the chart.

Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)
– Freezing Rotation (Optical Illusion)
– Reverse Spoke Illusion (Optical Illusion)

Excel Optical Illusions Week #23

This week’s Excel Optical Illusion is called The Freezing Rotation.

This animated GIF does not do justice – the workbook animation is much smoother.
As Michale Bach describes this illusion in the his page that inspired me…
… you see (1) an inner rotating part (the text) placed on (2) a rotating disk made up of coloured dots. The outer disk does not rotate continuously, but ‘swings’ back and forth. What is the motion of the central text? Is is a smooth rotation?
Or doesn’t it rather ‘freeze’ now and then, depending on the outer rotation?
My Excel version is a collection of shapes that are being animated by VBA, sporting easing. The VBA is dead simple so please download the file to see how it is done.
Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)

Excel Optical Illusions Week #22

This week’s Excel Optical Illusion is called Perpetual Collisions. The original work by Arthur Shapiro and Emily Knight was a 2008 finalist at the Best Illusion of the Year Contest, held by the Vision Sciences Society.

Here is the description of the Perpetual Collisions Illusion directly from their entry:
In the perpetual collisions illusion, the pink and the yellow columns seem always to be headed towards (or away from) each other, but they never meet (and they never grow further apart). Actually, the colored fields are completely stationary; an appearance of motion is generated by the spinning black and white diamonds located alongside the columns. Click on the button to add diagonal bars and remove the edges from opposing diamonds. Notice that the information at the edges makes the colored fields move diagonally, yet when the bars are not there and all the edges are visible, the fields move horizontally.
My Excel version (pictured in the animated GIF above) seems to work well in Excel 2002, 2007, and 2010, although I had to add more formulas just to support Excel 2002.
The chart is an XY Scatter type using inserted Excel shapes as the markers. When using compound shapes as markers, it is very frustrating because Excel changes the shape ever so slightly when copied to the chart’s data series. I experienced the exact same frustration when I was crafting celtic muse and those tiles are much simpler than these. It took quite a bit of trial and error to get them working as well as they are. It’s not perfect, but it’s close enough! I’ve included the tiles below the chart if you want to have a whack at it.
All of the series are fed from named formulas. The formulas that have a name like frame_[n]_y_coords are there only because Excel 2002 required them in order to not display a frame’s markers when that frame was out of scope. So adding these names enabled the chart to work in all versions. Likewise all the -100 values in the formulas are a requirement of Excel 2002.
The arrays for the series use two different techniques in their construction. There are four frames in the animation. The frame marker series array is constructed by multiplying together two constant arrays and then we just use INDEX to get the appropriate column for each frame. The diagonals series on the other hand is created by a completely different technique. Can you figure it out?
For such a simple display, this is a pretty advanced Excel chart and well worth your study time.
So what is your impression of the Perpetual Collisions Illusion chart?
Here is the file.
If you like my blog, please be sure to sign-up for the new Excel Hero newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)
– Two Sinusoids (Optical Illusion)
– Perpetual Collisions (Optical Illusion)

Excel Optical Illusions Week #21

The Excel Optical Illusion this week is an interpretation of an award winning optical illusion. It is called Two Sinusoids. It captured 3rd place this year at the 6th Annual Illusion of the Year Contest held by the Vision Sciences Society.

A very interesting thing happened. As you know, Hui has submitted several works that I have published, and I thought I should let him know that I had already replicated this illusion in Excel, in case he was thinking of doing so. I sent him an email and he shot one straight back, saying he had done it too and was preparing to send it to me! Yikes.
As always, he did a fabulous job and so I will make both available for you to download. Here is a picture of mine:
There are six different ways for your brain to interpret this image. You can see what look a little like American footballs scrolling to the left. Look closer and you can see the whole thing turning toward you like an auger on its side. Keep looking and it will start to spin the other way.
There are three more interpretations, but I’ll leave them for you to explore with the downloads and the original.
Hui and I both used the concept of multiplying frequencies to produce our respective versions, though we implemented that idea in very different ways. Both are highly iterative charts with lots of options. You can adjust the two frequencies and produce an infinite number of harmonic patterns. In my version I put a couple hundred of these interesting patterns into a gallery and you can interactively display random patterns from the gallery. It’s very cool.
Both of our charts are of XY Scatter type. I used named formulas for the series. Hui used worksheet cells to do the calculations that feed his series. Both use VBA extensively.
Mine will work to a degree in older versions of Excel, but some of the interactivity will be disabled. I’ve tested it in Excel 2002, 2007, and 2010. It looks best on 2007, and for some mysterious reason, the animation is quicker in 2007 than 2010. From everything I’ve read, it is supposed to be the other way around. Since it is so fast in 2007, I added an option to include a border on the data point markers, which really slows it down. The animated GIF above was recorded with this setting on. It is much, much faster with it off.
Hui’s version is for 2007+ only.
Here are the workbooks.
Daniel’s version:
Hui’s version:
If you like my blog, please be sure to sign-up for the new Excel Hero newsletter. Subscribers receive all of my articles AND extra Excel Hero tips.
Why do I share these optical illusions? The techniques that are used to make them, when mastered, can be used in many other Excel projects, in charting, formula crafting, and formatting. Learn them. They will aid you on your journey to become an Excel Hero.
Here is a list of other Excel Optical Illusions here at Excel Hero:
And here’s a list of other animated charts on Excel Hero:
– Excel, A Presentation Platform (Number Spiral)
– Lilac Chaser (Optical Illusion)
– Stereokinetic (Optical Illusion)
– Illusory Contours (Optical Illusion)
– Breathing Square (Optical Illusion)
– Enigma (Optical Illusion)