Excel Lissajous Curve Explorer

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My posts often contain charts where the data for the series is generated on the fly, but not in worksheet cells. Rather they are generated from named formulas. The technique deserves some explanation.

I put together a Lissajous Curve Explorer and Gallery to demonstrate how this works. Lissajous curves make a good subject matter for this demonstration because minute changes in their parameterized variables can produce an infinite variation as the output. 

Each plot in the Explorer contains 4,000 data points. Using named formulas to generate the data saves us the hassle and tedium of maintaining 8,000 cells of chart data (4,000 for x and 4,000 for y). Many of my projects contain dozens of series for a chart. In fact the Optical Illusions #4 had nearly the maximum of 255 series in the chart. So you can see how the number of cells to drive a chart could really add up. This technique avoids all of that.

What I do is create a named formula, n, to represent the number of points I want (this can be a constant or a formula).

The next step is to create a named formula, t:


In the Lissajous Curve Explorer, we are going to feed the trig function SIN so our t needs to vary between zero and 2π. This produces, in this case, 4,000 equally spaced values for t.  Using ROW/INDIRECT is the same technique that we use in normal array formulas in worksheets to produce a loop - remember that all named formulas are in fact array formulas.

Next we define the names, a and b, and link them to two worksheet cells so our users can enter values for a and b.

Next we define the named constant, δ, as π/2; and set _A and _B both equal to one.

The last thing is to create our named formulas for x and y:




That's it.  All we need to do now is create an XY (Scatter) chart with smooth lines and define a series:

Series name: ="Curve"

Series X values: =1!x

Series Y values: =1!y

Now we can plot an infinite number of Lissajous Curves using essentially no worksheet cells whatsoever. As part of the Excel Lissajous Curve Explorer I have included a gallery that you can scroll through to see a couple hundred of the best variations (in my opinion) that I've discovered thus far. You can edit the gallery by supplying values for a and b over in columns AB and AC on the worksheet. 

I've provided a scroll control to allow for easy navigation through the gallery. You can also toggle to User Select for direct input of a and b values. There are scroll controls there as well.

If you find a Lissajous curve that you really like, tell me the values of a and b in the comments and I'll try to add a web gallery to this post!

Here's the workbook:

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You can also use the Evaluate function in names to give more flexibility, so that the user can type(select) the formula in the Cell and the graph can be plotted based on the formula typed/selected by the user.

@Sam -

Thanks for commenting again!

I've always loved Stephen Bullen's method, but there are a couple of problems with it.

First I concentrate on Excel 2007 and using the Excel 4 XLM Evaluate function as the basis of a chart in Excel 2007 does not work properly. Well, that's not precisely correct - it works fine - but Excel 2007 complains bitterly at every recalc with a useless message that says, "A formula in this worksheet contains one or more invalid references." I've never figured out a way to make it work properly in Excel 2007 other than totally disabling warning messages, which is not exactly kosher.

It is interesting that his method (when setup properly) works without warning messages in earlier versions of Excel. I would say that's a bug in 2007.

The second problem is that since the function is from XLM, Excel considers it a macro. While I personally love VBA and make extensive use of it, many clients have policy forbidding macros completely. So I always try to take an idea as far as I can without VBA.

I think my method is nearly as good, since a user can still enter just about any formula, and have it charted without miles and miles of worksheet formulas. And in many circumstances it's preferable to have the equations hidden from view (yet still accessible via the names dialog). Finally, my way works in all versions of Excel.


Daniel Ferry

Did not realize that there was a problem with 2007.... seems to be in fixed in the 2010 beta.

But I agree using XLM is kind of risky with MS hinting that its going to finally go beyond 2010.

MS has also promised to finally complete the migration of XLM to VBA.


Hi Daniel

Very interesting use of range names for simplification. I'll have a play myself and see how I go.

Neale Blackwood
EHA homework

Hi Daniel,

{Comment as part of home work assignment}

It is fun to play with these figures. I recreated the graph with your methods, but only using the named formulas for _A, _B, a, b, n, t, x, y, t and δ. I then added a small VBA routine to change the a and b values like so:
Sub LissaJousChange()

Dim i As Long
Dim j As Long

For i = 1 To 30
Range("a") = ((Range("a") + 1) Mod 17) + 1
Cells(1, 1).Select
Range("b") = Range("a") + i
Cells(1, 1).Select

End Sub
Apparently to see the graph changing it is necessary to insert the "Cells(1,1).Select"-lines in the routine. I will play around a bit with different ways to change a and b and see if I can come up with some nice animations.


As always very interesting.

I've played around with your workbook for this several times in the past, but now I understand how it works thanks to the bonus segments.



Its nice to finally understand (very nearly) how you do this. This will enable me to push my charting endeavors many steps forward.

EHA student

EHA Homework2


I've been trying to make this work for me but for some reason I cant figure out I'm unable to make the charts work with the named formulas. I know I must be doing something wrong but I still don't know what.

This is the first time I've tried charting with named formulas.

I think I need help :s


Took me a while to figure how to do this, and was thinking of a way to 'scroll' through different values and you had already made a nice little macro to do just that.

EHA student

BOOYAH! I created a chart using named formulas! It took me some time to get it working, but I did it!

I've been here
Ian Huitson

This reminds me of a DNA string.

(EHA Student)

Very cool. Off to attempt my homework assignment. Wish me luck!

I finally understand this article now. And furthermore i finally see just why you name values and formulas the way you do. I had lots of fun on the homework, but learned that the 'line smoothing' that excel does is not great. I'd love to hear more from you about just what excel is doing when its smoothing.

Jesse (EHA)

Amazing stuff as usual. Thanks Bruce (EHA)

This is brilliant 16 and 16.1 is pretty cool - Bruce (EHA)

I understand this better now. I assume that "a_" is 10 times "a" only for convenience of having integers in the scroll bar settings?

Suprising I get this but that is only because of the very good bonus modules.

Kim (EHA)

Never thought we could do things like this
(EHA Student)

In terms of math, this was an excursion into alien, long forgotten territory. Looking forward to tackling the assignment!
Ulrik (EHA)

I really like the fact you can do this all without any data except the driver cells on the workbook. I'm looking forward to try it out in the Homework

EHA Student

Looking forward to having a play with this tonight in conjunction with module 2 bonuses.


Here is what I learned.
(1) Named formulas can return an array in memory.
(2) You can perform calculations on "arrays" stored in memory and return a different "array" stored in memory.
(3)However the arrays must be of the same size therfore a constant or formula must control the size of ALL arrays to assure they are of the same size.
(4)Chart can use an array stored in memory---- it does not need to be visible.
(5) Of course all this is accomplished by using Named Formulas to "access" the stored array.
This is the biggest "wow" factor I have learned so far in this course.

Here is what I didn't learn
(1) Theory behind the Lissajous curves
However they look "good".


yep it's beautiful, but I must say am more than a little bit disappointed. For me, Excel is a business tool and I didn't think of that much maths.

I really like the idea of arrays stored in named formulas and especially using them with charting and saving cells in the workbook but I truly hope that we don't get any deeper into this trigonometry stuff because it's way above my horizon. I have no single clue how to find a formula, I could not even follow the example you lay out above. Last maths classes are 20 years ago and never needed any of these trigonometry etc. ever after.

Sorry, but I really have to say I am really disappointed.

Excellent as always!

I really enjoyed learning about this technique and think I'll be able to make good use of it.


Overwhelming but so exciting! i thinkI want spend my days playing!

EHA student-Michele

Cool stuff and your explanation has certainly made this toughie a bit more approacheable....Thanks
EHa student {Sriram}

This is really inspiring, I am going to study this worksheet more.

I bet this would be really neat to watch with chart animation to interpolate through the gallery.


Very cool demo of the concept.
Kim (eha)

EHA assignment. Read and getting on with the work.

Hmm, very interesting. I will give it a shot.


Interesting article. While I get the concept I'm still working to understand the details. Practice, practice.

Bryan (eha)

Cool. Overwhelming!

i was here. thanks for the lesson.
ryan (eha)

The example is great, all I had to do was take the math on spec.

Ingenious ... very clever way to simplify some very tricky calculations

(EHA student)

okay, read this ... now on to the homework.

Wow...now to try and recreate it.

Very interesting exercise

I was here in the way to becoming Excel Hero!


Victor Andrade

Finally getting caught up. Happy Thanksgiving!

Ditto on that, @edmundfry! Thanksgiving is a great day for catch up!

I agree too Mark!!!
KW Slate

Great stuff. I sure have a lot to learn...

Awesome stuff. Now on to HW #2.

I agree with everyone on finally getting caught up. Surpriosingly this seems to make a lot of sense. We'll see if I feel the same way once I put the graph together.

Well, I finally found the time to catch up. Great stuff!

Checking in after a delicious Thanksgiving vacation.

I am finally catching up also. Feeling overwhelmed after this.

Catching up. I remember this post - eye opening!

EHA Module 2 homework

IIRC I tried to follow this example after seeing it in the Benfords Law chart. This time it actually makes sense (I'll take the maths part as read). Would love to figure out how to draw these curves between two points on two axes.

I'm having a problem getting the formulas into the chart series (I'm using Excel 2007 if that is relevant). I put in the chart title fine and the x-axis series fine (referring to the formula), but when I try to put in the y-axis series, Excel won't let me leave that box (no error message or anything, it's just can't click on anything else; hitting enter doesn't work either). It doesn't seem to be a problem with the y formula, because I can put it into the x-axis series just fine.

Has anyone else run into this problem and fixed it?

Thanks for the great blog postings- very informative.

EHA2 Mod 2 Homework

I've read this before, Daniel, but now I can begin the process of understanding it. Thanks for the great job so far in awakening Excel for me.

Fascinating material! One question before my head throbs any more... Is using a named (array) formula as a chart series, as opposed to a named rage of cells, new to 2007? I cannot get it to work in XP to save my life. Once again, I'll try it again at home tonight on 2010, but was just wondering if you knew if this was an issue, or just me?



Hi, Jay.

It works on all versions of Excel.

Don't forget to anchor the named formula to a worksheet in the chart data series by specifying the name of the worksheet and the exclamation point prior to the name!

Excellent stuff, now I'm off to do my homework.

EHA2 Student

as always with your articles, it looks deceptively easy :) and as always the proverbial devil will sit in the details :) I cannot recall when was the last time I was so excited about doing the homework!

Marcin "kuty" Markiewicz
EHA2 student

Hi Daniel,
I got it, it was a long day, yesterday. I came back fresh and got it on the first try. Pretty amazing concept, I never dreamed a chart could have a life of its own like this. It's homework time, now...

... I don't get it, but I am sure I will understand soon. I already no what route I want to take with the homework and can't wait to use the name formula technique.

@jmar I had the same problem. Don't forget the '=' sign: =Series1!x and =Series1!y

Hi Daniel,

This is starting to sink in, I keep going back to the lecture material trying to understand how the charting still works even after deleting the individual data points! A very powerful concept, one I intend to grasp at a deeper level in the next couple of days. I believe I have a good foundation for diving into the homework now!
EHA2 Student

@Daniel Well, that was fun. Was able to reproduce.

Yet another excellent article of how to do an eye-catching workbook without much work.

EHA2 Student

Great article. I will have to go back and read again. The EHA is introducing a lot of new concepts and possibilities in Excel for me. Thank you,

Agreed,, this is new in concept to me, and i do appreciate these types of stretch activities,, that's how we grow :o) Thank you Daniel.

Great stuff. The Lissajous curve is obviously highly sensitive to the a/b ratio. I also found it interesting how sensitive the curve was to the value of n for a/b > 1 or 2. Playing with this value produces some interesting curve variations.


I wish I could say this was illuminating, given the other comments it must be but to me it may well have been written in Chinese and my chinese is limited to ni hao

I will now give the assignment a shot

EHA2 student

That was a fascinating dimension to try and think in. Now I've got to get my homework done!

Seemed overwhelming until I figured out that you're just doing variable assignments within the Name Manager instead of pasting data across the ranges. Pretty nifty application of technique!

Makes sense and very straightforward. Thanks, Daniel.

Scott D. (EHA)


Lovely graph, better technique.

Simon (EHA)

Though now I understand the technique behind this mathematical artistry I must confess my did not spend much time in understanding the formulas.
I will appreciate if you can demonstrate the application of this technique in the context of Business Analysis and Financial modelling

Haider (EHA


The lecture on graphing and this graph are very impressive.

This is a very powerful technique. While Dan points to the benefits in speed, for where I work, it's a way of cleaning up cluttered sheets. All hail the Named Formula!

Very cool and impressive. I've read the article and looked over the code but I'll admit I'm going to have to spend more time re-reading and pondering this one before I can say I really understand it well enough to use the techniques myself.


Smooth graphs! The math is challenging me and I admire the very clean technique.
Please explain the reason for creating two named formulas "_A" and "_B", both assigned the constant 1. Is this a quick way to alter the size of the graph? I tried 0,5 and 0,75 to see the graph grow in size.


This is a great concept and will take me quite some time to digest. Love learning all these new ways of doing things.


This is a great concept and will take me quite some time to digest. Love learning all these new ways of doing things.


This makes sense when I’m reading it, but trying to put into action is quite another matter!

-- ajp

EHA2 Homework. Read it. Chewing.



Pretty ground-breaking stuff for most of us - I had no idea named formulas could be combined with charting in such a powerful manner, and the last example in the Mod 2 lectures was fabulous.

Tried to recreate the worksheet on the fly, but did something wrong, so I will slow down, do it again, then tackle on of these mathematical function challenges.

EHA2 Student homework - gotta love it!

Kevin DeWhitt

Starting my homework now... let's see how much I understood of this.

Really interesting on the power of excel

Its unfortunate I don't have any maths experience to understanding these formulas, so I will see what I can use from the day to day stuff I deal with.



Really amazing. As long as I have been using Excel (~15 years) I feel like I know just a fraction of 1% of what there is to learn after reading posts like this. Even though I do not understand the formula's contained in this article, it is the concept of charting with just formula's (and no data) that is very intriguing. Now, to try and put it into practice.



As always, an impressive post. Demonstrates yet again the power of NAMED FORMULAS. However, unlike some of the previous lessons, I can't see how I'll apply this to financial and statistical reporting and analysis. Is there a time one could use Named Formulas with charts when the material is given rather than formulaic?

John Noble

At first I thought this was way over my head.
But I did manage to produce a beautiful chart for my homework, so I guess I did get the general idea. As long as somebody else provides the maths formula I need to use.


Fascinating. This is going to take some practice. Homework, here I come.


Most interesting, although I never got into Calc or Trig in school. I can't imagine what I would ever use this for, but it's a useful exercise in seeing how the use of named aray formulae simplify, or rather optimize the chart's input data series.

Very intriguing. I'm learning I don't know as much about charts as I once thought. Looking forward to more homework....

I understand the individual words, it's just when you put them all together I get lost! Time for some serious study.


Another great article as always Daniel.

Chris D

Don't know how you arrived at the formula for t, but got everything else. Going to start homework now.


Good Article Daniel.

Wow. I need to get my head around this.

Very nice - I had the odd glitch though as I don't think the VBA turns off recalculation as the sliders are moved & Excel struggles to keep up!


It's very impressive. I think a=46.9 and b=70.3 looks like a squashed fish.

The named formula stuff is incredibly powerful, though the statistics part is beyond me.


It's a LONG time since I've seen (or used) equations like that. Wow.
But it's the Charting that REALLY impresses.
MOST interesting...

Peter H, EHA2

I've already learned so much and I'm not even through the second module. Just love this class, Daniel!

Mike, EHA2

Wow. Again.

Billy W, EHA2

Generating charts and replacing cell data completely with named formulas takes Excel in a whole new direction. Thanks for sharing! Steven (EHA2)

Read several times now and always rewarding.

- juanito EHA2

I've watched the videos about 5 times now and I get the concept and love it though I'm scared witless about the practical application of it in case I'm fooling myself. Will soon know!!!

Hugh EHA2

Another very interesting concept and the course is just getting started :).

Thanks so much for everything thus far.

Tai Du Luong

A good illustration of the charting skills you teach us in Module 2! Thanks Daniel.

Johnny Tam, EHA2

Great article!
-Bonnie, EHA2

Very interesting. The more I learn about named formulas the more I am able to see possibilities.

Hi Daniel!

Impressive post and chart! I am just wondering how I can speed up my charting and simulation skills after learning named and array formulas...


rbertin, EHA2.

Still in a fog...
Thanks for the example. It will help, I'm sure.


The chart is impressive, I'm waiting for it to sink in, I'm sure practice will help :)

Impressive never seen anything like this, eager to learn how to create this typr of chart. Thanks, Torrevio

I have been playing around with this, but have yet to work properly. Still working...

This is really incredible in its simplicity and seemly infinite outputs.
thanks for sharing,

This is amazing stuff. I found this easy to understand after doing Module 2 in the EHA course.
Phil, EHA 2

Example makes it very clear.
David, EHA2

a=86.5, b=29 is particularly attractive to me for some reason.

Thanks for the revelation.

EHA3 Homework

Thanks Daniel. Great graphs and very instructive method.

I liked ndxGallery=9 (i.e. a = 2 and b = 1.5) and then varying δ.

Try δ = -10, 0 , +10


interesting article. Great creating a series on the fly.

PS: A little bit of trivia. The logo for our ABC (Australian Broadcasting Commission) is a Lissajous curve (a = 1, b = 3, δ = π/2).


Nice article.
Last time I built a lissajous curve was in the electronics lab classes back in the 80's. But that was made in an Oscilloscope !
This is a technique that shows us the phase shift between two signals according to the curve that appears in the screen.
Here is an illustration about how it works
Marcio Quelhas
EHA3 student

Very nice idea.

Chol (EHA3)

Very nice idea.

CHol (EHA3)

Very Cool

This technique will allow me to reclaim a lot of "real estate" in my workbooks.

KenU; EHA3

Great technique and nice graph explorer. Now off to borrow some of these ideas for my EHA3 HW.

Leaving a comment as requested for EHA3 homework. Nice choice of curve to illustrate the point by the way.

I am really impressed with this new method of charting. Before i would hide the data or have it in a different sheet, etc....no need for that anymore. thanks.

Ok I have read this for EH3 and now need a couple of expressos to tackle the homework!

Using this approach operations are definitely faster but I am struggling to present them to others: "usual" excel users are expecting to see values and be able to check them for correctness. Not exactly straightforward with this WoW

This article again makes me completely reevaluate how I have been using Excel. Not having to create huge tables of data will save a ton of time. And I still think that I'm only grasping a very small portion of the power of this new way of thinking.
EHA3 - ndarmyserver

Hey Daniel! This article, along with EHA, is extremely informative and concise. I am looking forward to future modules. (EHA3)

Very impressive.

I'm having difficulty in getting Excel 2010 to accept =ROW(OFFSET('1'!$A$1,,,n)), where the '1 is assigning Sheet1. So far the only way I've been able to get things to work is literally using Sheet1, i.e. =ROW(OFFSET(Sheet1!$A$1,,,n))


Very interesting; daunting and a bit overwhelming though. I've never used named arrays (with or without charting). The idea's behind it are great. I'm going to give it a try. Wish me luck.

Powerful concepts -- it will be interesting to try them out in the homework assignment.

Steve Porter (EHA3)

Very interesting concept, I can see a pitfall, for myself at least, in that not readily having datapoints to view may cause difficulty in recognizing errors in some charts.

I love the idea of using named formulas in charts. It was a pain to plot an equation calculated in a range of cells and having to change manually the size of the range wnem the parameters were different.

I love the idea of creating a series with ROW. And some of the magic tricks we have seen in the videos.


Amazing chart. Really enjoyed replicating the model myself. Thanks! D_BELLIZZI EHA3

This is a very interesting topic. I've learned a lot.

Bob Kennedy

I read it and follow it step by step.
I can't create the same thing as you attached to the post. The chart will not accept me putting "=!1y" there. It doesn't pop up any hint for reason why it will not accept it. I clicked "ok", it will not process to another step. It seems something is wrong. I compared mine with yours, can't see any difference on the named formula. What could be wrong?

Hi siyingruan.

Remember, yuou must anchor the chart to a worksheet.

This is done between the = and the ! characters.

You have this:


But if your worksheet is really named, "1", then it should be this:


By the way, I like when a=42.7 and b=10.7.

I named the worksheet "1", the "Edit Series" window accepts "=1!x" but doesn't accept"=1!y".


The more I dig into our homework, the more lost I seem to get! I clearly see now that the amount I thought I new about Excel is in effect very minimal compared to what I'm working on wrapping my brain around from these past two weeks! The charting is really cool, I had no idea it could be done without hundreds's of thousands of cell data points. This will definately keep my brain cranking while digesting it.

Bill Roberts
EHA3 student

Daniel - great article, although I wish I remembered trig better! Looking forward to putting together my own chart.


Daniel - Incredibly clever! EH3 homework still to do. Totally understand the named formulas, but struggling with the maths. Will get there though!

Great article... working on the homework assignment.

This blog article along with Module 2: Lecture 5 of your EHA course is beginning to sink in! I'll see what I can do on the homework now.

EHA3 Student

Daniel, I keep rereading the article and trying to understand. The math is a little complex for me. It has been too many years to count since I took those courses. But the curves are really cool and the fact they are crated without thousand of data points is for me just amazing. I still need to go back and work more on the homework.
EHA3 Student

This is very cool, so powerful. I hate math, so this is not my idea of fun, but cool just the same.


This is a method that had never even entered my mind before. Thanks for yet another "horizon expanding" technique!

I used to think I was proficient at excel. Then I met Daniel Ferry, heard about Lissajous Curves, and named formulas. Going to try the homework now.

As much as I read, I realize that there is still too much more to learn from Daniel. By the way, I'll need a review of Module 2 before homework.

Looks like I will have read this a few more times before in sinks in. The Homework will have to wait.

Wow! It's been a long time since trig! Really digging deep to get those synapses to re-fire! Totally getting tho' that once I can master this that it will have profound implications for my work which doesn't include the trig stuff... at least not now!Thank you so much! Off to start thinking about the homework.

EHA3 Student

I now understand the use of named formulas and arrays to provide data to charts. However getting more familiar with the advanced usage of ROW(), INDIRECT(), and OFFSET() will take more examples and projects -- which I'm sure we'll be seeing soon.

EHA3 Student


This is great. My mind keeps thinking of the possibilities...

Thank you,

EHA3 student

Now the challenge will be to create my own!


EHA3 student

Nice one...
EHA3 student

Very impressive work, Daniel. While I can see a use for named formulas in my future charts, I'm not sufficiently schooled in the ways of mathematics to wrap my head around this one.

EHA3 Student

Wow! I am impressed with the Lissajous Explorer and am looking forward to learning new chart techniques in the modules to come.

EHA3 Student

Your Excel knowledge is truly incredible!!! I'm blown away again.

EHA3 Student


EHA3 Student

Hi Daniel,
Trying to get my brain round it after many years of excel/VBA coding. Still new things to learn.
That's why I'm here.


Still trying to absorb this. Thanks a lot.

EHA3 Student

Great application of these charting concepts. Could have used a little more background on the math side.
EHA3 Student

Great approach! Thanks for revealing the named formula abstraction layer of Excel, and walking through it step by step!

Really enjoyed this article and the examples!

Interesting article. Going to try a chart with only named formulas now.

I know this is not the answer you expected :-) - but this is so beautiful.....and I want to play with it now..

I agree with Anne!

Just finished watching the last module 2 lecture and reading this article now I cannot stop thinking about the many ways I can use this.

Jon O.

wow, I never knew you could do this type of stuff in Excel!! Wish I had known about it in college!

Wow! lots to try and assimilate

Only week 2 of EHA4 and already the superlatives are inadequate :-)
Two aspects stand out - the SPEED of the approach and the simplicity of the HOUSEKEEPING required.
Next question....
How to 'un-learn' so many years of inefficient Excel use?
Brilliant, Daniel!

Simply Excel - lent. Much more robust than I ever imagined.

Very nice! Reminds me of peering at Lissajous plots on the lab oscilloscope in college...like the automation in the worksheet.

EHA4 Student

I'm fascinated by the Lissajous Curves. Quite beautiful results. I'll now try to this exercise work using something I'm more familiar with: financial formulae.

Using named formulas is awesome! I never realized their potential.

You make it look so easy. I hope someday it will all make sense to me and be just as easy.

I had no idea graphs like this could be made so quickly!


I have watched all the videos and read the Excel Lissajous Curve Explorer article. While I have not yet applied with practice, my understanding is just emerging. I want to go back to the INDEX and work forward from there.

Amazing stuff...a lot to wrap my brain around!

Cool Stuff the example file awas really cool.

find it all quite interesting, but beyond my maths. But it does make for very elegant charting. Looking forward to the homework.

Pretty, but beyond my comprehension.

Very beautiful and really hard to undestand

got the concept of charting without cells but the math is beyond me at this point

As part EH4 homework, I read the article and played with the gallery. I really liked the curves produced at a=79.9 and b=61.5, 62.8 and a=80.8, b=71.4.

The graphs are terrific. Just need to get my head back into high school maths mode.

One word... Radical


The math is a bit more than I'm used to, but the functioning of the worksheets was informative. Thanks.

Hi Daniel, the maths is way too complicated but I am now building some interesting graphs!


Great article...I am totally lost at this point, but great article.

I enjoyed the article. Now to see if I can do this myself.


That's very cool!

Very cool - wish I had been able to use something like this when I took trig!

I'm starting to beome more comfortable with named formulas and array formulas. Now I need to think of what to do for homework! Creativity is not my strength.

Bermir was here.
Interesting stuff. I am sure this charting without cells links in some way to how I (will) use Excel. Now I just have to figure out how :)
Hope the homework will help in that respect.

The amount of possibilities with such simple user input is pretty awesome. Must perfect!

This is beautiful. I have a lot to learn.

Article is very interesting. I have yet to grasp the details on that one though !

Good exercsie for familiarity with naming formulas and their relationships. ...without "having" to understand what I really did. ...yet.

This is really cool. I get the formula part, but I am still having a time understanding how to set it all up. I think choosing what order to name all the arrays is the most difficult part.

Wow, those look great! Amazing!
Dmiller - EHA4

Great stuff. I am really confused at this point and need to work some examples for the light to go on. I am looking forward to raising my understanding of excel beyond advanced user to super user.

I liked a=100, b=57!

Charles M

I am amazed by the insights you have for efficiency.
Anthony, EHA4

Very interesting charts and methods to draw without using cell!! Very powerful.

Najmuddin (EHA4)

While this is not a deal breaker, but the example actually uses 4001 values (0 to 4000). Realised while I was trying to figure out the n+1


Pretty slick! Are you going to show us how to do those cool slider bars?

Very cool. a=100, b=88.8 looks like the pattern on my couch. Not the color though :)

Very elegant, great demo!
EHA5, Roger

Cool... I'm officially overwhelmed now :|
EHA5, Jon

Possibly the coolest thing I have ever seen!

LeslieR, EHA5

Who ever asked the question in high school when they'd ever need to know this stuff in real life now has an answer! Great work.

Absolutely the coolest thing I have every played with in Excel. Daniel, you are the wizard!

Clare, EHA5

My brain is slowly working through how named ranges can do this sort of thing and whilst there is still a way to go I do see just how useful it can be

John M EHA5

WOW! It is amazing what can be done with Excel!

Dumbstruck at what the possibilities with Excel are, now that I have seen this.
Darren, EHA5

Article read. Mind blown. ALL of this is so new. Off to try and practice.

Amazing! I cannot wait to try this in a realworld application.

As on old number cruncher, this is an entirely new application of Excel's abilities. I don't have much use in my normal day-to-day activities, but fascinating.

Guess I should have paid more attention in my high school geometry class. I'm not even sure where to begin with this homework, but I'll give it a shot!

Very interesting. Can't honestly say I understand it but very interesting.

Cheers - was here!

Very interesting

I don't even know where to begin with this, very cool what you can do though.

This is very cool to see but I am not sure what I am looking at. I also don't know who or if this would fit into my current uses for Excel - if I could use is it how would I know the formulas and math equations.

Interesting stuff. New to me though so I will have to spend some time working through it.

Lsmith, EHA5

interesting stuff

Mind-boggling stuff. You're an Excel genius!


It's really amazing! I have never thought that it was possible to do something like that in excel. Thank you for sharing this!

Still letting the concept sink in. Thanks for the awesome content.
RicardoT, EHA5

I'll echo everyone else that this is pretty amazing. Still trying to fully grasp the power of named formulas.

Kyle, EHA5

Wow - that's brilliant. Thanks for sharing it.
Sharon, EHA5

Man, this is incredible!
I'll try to digest all this information...lol

A lack of personal context is making this a little hard to grasp. Looking forward to practical usage.

Was able to recreate this and play with values based on your formulas. Like Colby said, some "usage time" will create a pratical value.

Each video of every module is providing more and more clarity. This application is a nice practical step. Looking forward to more examples.

My vote is for a = 50; b = 50.7

Very impressive. You've inspired me to do some kind of sinusoidal pattern for my module 2 homework.

Josh (EHA5)

This is a pretty spectacular formula! My favorite combination is a = 66 b = 57.7

BenV (EHA5)

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This page contains a single entry by Daniel Ferry published on March 29, 2010 3:30 PM.

Excel Optical Illusions #6 was the previous entry in this blog.

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