The Cantor set is a special set of numbers lying between 0 and 1, with some fascinating properties.
It’s created by removing the middle third of a line segment and repeating ad infinitum with the remaining segments, as shown in this gif of the first 7 iterations:
The formulas used to create the data for the Cantor set in Google Sheets are interesting, so it’s worth exploring for that reason alone, even if you’re not interested in the underlying mathematical concepts.
But let’s begin by understanding the set in more detail…
What Is The Cantor Set?
The Cantor set was discovered in 1874 by Henry John Stephen Smith and subsequently named after German mathematician Georg Cantor.
The construction shown in this post is called the Cantor ternary set, built by removing the middle third of a line segment and repeating ad infinitum with the remaining segments.
It is sometimes known as Cantor dust on account of the dust of points that remain after repeatedly removing the middle thirds. (Cantor dust also refers to the multi-dimensional version of the Cantor set.)
The set has some fascinating, counter-intuitive properties:
It is uncountable. That is, there are as many points left behind as there were to begin with.
It’s self-similar, meaning each subset looks like the whole set.
It’s fractal with a dimension that is not an integer.
It has an infinite number of points but a total length of 0.
How To Draw The Cantor Set In Google Sheets
To be clear, the Cantor set is the set of numbers that remain after removing the middle third an infinite number of times. That’s hard to comprehend, let alone do in a Google Sheet 😉
But we can create a picture representation of the Cantor set by repeating the algorithm ten times, as shown in this tutorial:
Create The Data
In a blank sheet called “Data”, type the number “1” into cell A1.
As we drag this formula to adjacent columns, the relative column references will change so that it always references the preceding column.
In column B, the output is:
Then in column C, we get:
And in column D:
This data is used in the sparkline to generate the correct gaps for the Cantor set.
Draw The Cantor Set
We’ll use sparklines to draw the Cantor set in Google Sheets.
Create a new blank sheet and call it “Cantor Set”.
Next, create a label in column A to show what iteration we’re on.
Put this formula in cell A1 and copy down the column to row 10:
="Cantor Set "&ROW()
This creates a string, e.g. “Cantor Set 1”, where the number is equal to the row number we’re on.
The next step is to dynamically generate the range reference. As we drag our formula down column B, we want this formula to travel across the row in the “Data” tab to get the correct data for this iteration of the Cantor set.
Start by generating the row number for each row with this formula in cell B1 and copy down the column:
(I set up my sheet with the data in columns because it’s easier to create and read that way. But then I want the Cantor set in a column too, hence why I need to do this step.)
Use the row number to generate the corresponding column letter with this formula in cell C1 and copy down the column:
In this tutorial, we’ll create a checklist template in Google Sheets.
We’ll use checkboxes, conditional formatting and a sparkline to build a checklist template like this:
Checklist Template Use Case
There are many situations when a checklist comes in handy.
From simple to-do lists to project planners, from teaching lessons to tracking physical goods.
And although this simple spreadsheet checklist isn’t suitable for large, complex projects, or projects that require more robust data trails, it’s a quick and easy way to add some useful flair to your spreadsheet projects.
When I teach live workshops, I often include a front sheet in my Google Sheet that I use as a checklist for the exercise steps.
It ensures I don’t forget anything and gives the audience a visual clue as to where we’re up to in the workshop. And I get almost as many questions about how I built these checklists as for the topic of the actual workshops.
How To Create A Google Sheets Checklist Template
Feel free to download the checklist template and make your own copy:
I’ve set my file sharings to allow anyone with the link to view this file. You may not be able to open this file because it’s from an outside organization, and my Google Workspace domain is not whitelisted at your organization. You may be able to ask your Google Workspace administrator about this.
In the meantime, feel free to open it in an incognito window and you should be able to view it.
1. Sheet Set up
We start with the checklist title on row 1, center aligned.
Then leave a blank row.
On row 3, we put the word “Progress” in column 1. Leave the other column blank for now.
Row 4 is blank.
On row 5, put the headers for the checklist table: Status and Step
On rows 6 onwards, we put a checkbox in column 1 and the corresponding step in column 2 of that row.
Firstly, the COUNTIF(A6:A, TRUE) function counts how many of the checkboxes in column A have been checked (i.e. have a TRUE value).
The output of this is a single number, between 0 and 10 in this example.
We pass that value into the SPARKLINE function.
Sparkline Bar Chart
Then we set the sparkline to be a bar chat, with the first option: "charttype","bar"
Next, we need to specify a maximum value for the bar chart, so that it can compare the count of checked checkboxes (e.g. 4) against the maximum possible number (10 in this example) to get the percentage completion.
We could simply type in the max value of 10 as an option, but it’s better practice to set it with a formula so that it will update automatically if your data changes.
To do this we count the number of “steps” in the column next to the checkboxes: "max",COUNTA(B6:B)
Finally, we set a custom color for the sparkline with the final custom option: "color1","red"
The charts themselves are a bit of a novelty. Yes, they’re aesthetically pleasing because of that resemblance to a real-world, tapering funnel, which reinforces their message, but a plain ole’ bar chart would be equally suitable and actually easier to read data from (because the bars have a common baseline).
However, they throw up some interesting techniques in Google Sheets and for that reason, merit this long article.
We’ll build them using tricks with the chart builder tool, then with two different types of funky formula and finally, and best of all, we’ll build a tool using Apps Script, as shown in this image:
As with the waterfall charts in Google Sheets, they’re not one of the out-the-box charts available to us, so we have to manually create them with a crafty workaround. Thankfully, they’re relatively simple to create, certainly simpler than the waterfall chart.
For all of these examples, we’ll use this fictitious real-estate dataset:
Here, I’m imagining the real estate agency collects data relating to their sales funnel, and they want to display it in a funnel chart format.
Click here to open up the Google Sheet template and make your own copy (File > Make a copy...).
Sparklines are small, lightweight charts, typically without axes, which exist inside a single cell in your spreadsheets. They’re a wonderful, quick way to visualize your data, without needing the complexity of a full-blown chart.
1. Collect user inputs through a Google Form into a Google Sheets dashboard
Google Forms are a quick and easy way to collect data. The responses are collected in a Google Sheet which we can then use to power a dashboard. For example, you could run a survey on customer satisfaction, or status reports from your operations team members, and then turn this data into a one page visual summary, giving you instant insight into your data. Let’s run through a super quick and simple example:
Next, setup your Google Form by giving it a name and adding any questions that you have. In this example, I’ve created a form with one multiple choice question which asks a user which color they prefer (from red, blue or green):
Step 3: Create the Google Sheets dashboard
View your responses and setup the Google Sheets dashboard. You’ll need to submit the form at least once, so that you have some data in your responses which you can use. I then added a new tab and created a new table (a staging table), which uses a countif formula (see section 3 on conditional formulas below) to tally up the votes for each color and show this count in the staging table. Then I added a bar chart and pie chart (see section 6 on charts below) running off this staging table to display the counts visually. These charts will update whenever new votes are submitted.
2. Retrieve data with LOOKUP formulas
Mastering lookup formulas is a key technique for many data projects in Google Sheets (and Excel). It’s at the heart of the Google Sheets dashboard shown at the start of this post and such a useful technique in it’s own right that I’d recommend investing time to practice this technique. There are several methods at your disposal:
VLOOKUP is a vertical lookup formula which searches the first column of a range, and when it finds the first instance of the result (if there is one), it returns the value in that row from the column of the range that you specify with the index value, e.g.:
This formula takes the search term in cell F1, for example a string “Channel A”, and looks for it in column A. At the first match, if it exists, (e.g. imagine cell A10 contains “Channel A”) it returns the value corresponding to column 4 of that same row (in this case D10, which might be a sales figure for Channel A). Searching through numeric or dates in your lookup column (the first column) requires the data to be sorted to avoid incorrect values being returned.
HLOOKUP is a horizontal lookup implementation of the vlookup formula. I find it’s rarely used but useful to keep in the back pocket for certain specific situations.
INDEX & MATCH are two formulas that combine together to create powerful, flexible lookup solutions. They are superior to vlookups by being more flexible and avoiding some of the pitfalls with vlookups (check out these articles here, here and here – they’re Excel based but still apply to Google Sheets). However, they are a little more complex to implement as they involve two nested formulas.
To create the same implementation as we had above with the vlookup, we could use this formula:
Multi-condition lookup formula: Sometimes a simple lookup formula isn’t enough. For example, you may need to find a result based on two or more parameters (e.g. web traffic from a specific channel in a specific month). In this case, a multi-condition lookup formula can do the trick.
Say we have this table of Google Analytics data and need to retrieve the number of Search results in January 2015 (i.e. our answer is dependent on three criteria):
Let’s assume we have setup a staging table for our charts below this. To lookup the value we want (in this case Search for Jan 2015):
Crazy huh! This formula was inspired by this post from Excel wizard Chandoo, and uses an index/match lookup to compare multiple values across multiple columns in a data table. It concatenates the year, month and channel, to use as the lookup value, then looks for this concatenated value in the raw data across the year, month and channel columns. When it finds the right match it returns the corresponding result.
3. Apply logic with conditional formulas
COUNTIF is a formula which counts items in a range that match the specified criterion. It’s useful for doing things like counting non-blank cells in a range or counting the number of specific items in a range. The formula is:
COUNTIFS is similar to the countif formula but returns a result based on multiple criteria. In other words, it counts the number of items in the first range that matches the first criteria AND also match a second criteria in a second range AND a third etc… The formula is slightly different to the basic countif formula, as follows:
SUMIF is the same idea as the countif, but returns a sum of the values. It’s possible to match criteria in one range, but sum values in a separate range, which is a really useful feature (e.g. imagine a table with names in column A and sales results in column B, then the sumif formula can sum the sales values for all occurrences of say “Ben” from the list of names). The formula for sumif is:
=SUMIF(range, criterion, [sum_range])
SUMIFS is the multi-criteria version of sumif, so it’s the same idea but the sum is calculated when you match multiple criteria in multiple ranges. Again, a very useful formula:
Dashboards often have a date component to them, where a variable changes over time and merits being illustrated visually in the dashboard. There are various formulas/techniques available for automating this process.
The today formula, which gives the current date, will display the date the last time the spreadsheet was recalculated (for example, when you open it or make a change). The formula is:
If you want to also have a current time element in your spreadsheet, then use the now formula, which returns the date and time the spreadsheet was last recalculated. The formula is:
Both the today and now functions can be set to update automatically, rather than just when the sheet is recalculated. Go to File > Spreadsheet Settings and then select “On change and every hour” or “On change and every minute”.
Be careful of inserting too many of these formulas in your spreadsheets as they are volatile functions, which means all that recalculating will harm your spreadsheet performance.
An example of using the today formula would be to display the current month in your dashboard, using the following text formula:
For a more complex example, think of setting up start and end dates for a dashboard table, where I could enter formulas using the today function, set it to update automatically, and then base the other dates off that, using formulas.
The eomonth formula comes in handy here, returning the last day of a month which falls a specified number of months before or after another date.
For example, use the following formula to create the first day of the month prior to the current one:
=EOMONTH( TODAY(), -2 ) + 1
I could then keep “rolling” the months back, by changing the “-2″ to “-3″ for two months prior, then “-4″, “-5″ all the way back to “-13″, to give the current month plus 12 preceding months in a table, which would automatically update as we move into each new month.
I could also get the first day of the current month but a year earlier, for example to compare current sales metrics against the same period last year, using the following formula:
There are many possible variations from combining today, date, text and eomoth formulas, to get the correct periods you want in your Google Sheets dashboard and have them update automatically to stay current.
Use data validation to add interactivity to your dashboards. You can create a nifty drop-down menu from which the user can select a parameter, e.g. a sales channel or specific time, and then change the data based on this choice, so any charts will update automatically. It’s a pretty simple technique but surprisingly powerful.
First, create a list of choices to present to the user, e.g. list of sales channels, and then using the Data > Validation feature on the highlighted list of values, create a user input menu for sales channels:
The user then has a drop down menu in your spreadsheet, from which he/she can select the desired parameter:
Data in the table which underpins a chart is changed based on the user’s choice from the drop-down menu above, by using one of the lookup formulas from step 2.
Google has a whole suite of charts available to use with your data. Some of the most well known are the plain old bar/column chart, the much-maligned pie chart (for and against arguments. Personally, I think judicious use is ok), line charts and scatter plots. In addition though, Google Sheets has the ability to create map charts, interactive time series charts, gauges (can be useful if used judiciously) or combined “combo” charts, which allow you to combine different data series visualizations.
The humble bar chart can be tweaked into a stacked bar chart, which can be used to visualize two related metrics, for example how many sales have been made so far, versus how many are still required to hit the target.
An area chart can be used to show comparisons of data, as shown in this example of the cumulative sales during a digital flash sale, showing 2014 data against 2015 data:
Sparklines were first created by statistician and data visualization legend Edward Tufte. They’re small, simple charts without axes, which exist inside a single cell. They’re a wonderful, quick way for visually showing a result, without needing the complexity of a full-blown chart. They work well for datasets based on a timescale.
A sparkline looks like this:
The formula for sparklines in Google Sheets is:
where data refers to a range of values to plot the sparkline. The optional options argument is used to specify things like chart type (line, bar, column or winloss), color and other specific settings.
Hidden in the Custom Number Format menu is a conditional formatting option for setting different formats for numbers greater than 0, equal to 0 or less than zero.
It’s a great tool to apply to tables in your Google Sheets dashboards for example, where the data is changing. By changing the color of a table cell’s text as the data changes, you can bring it to the attention of your user.
Consider the following sales table which has a % change column:
Now take a look at the same table with colors and arrows added to call out the % change column:
It’s significantly easier/quicker to read and absorb that information.
How to add this custom formatting
1. Somewhere in your Sheet, or a new blank Sheet, copy these three CHAR formulas (you can delete them later):
Now, copy and paste them as values in your Sheet so they look like column C and are not formulas any longer.
(You copy as values by copying, then right clicking into a cell and select Paste special > Paste values only…)
You’ll need to copy these to your clipboard so you can paste them into the custom number format tool.
2. Highlight the % column and go to the custom number formatting menu:
3. Change the 0.00% in the Custom number formats input box to this:
[color50]0% ▲;[color3]-0% ▼;[blue]0% ▬
as shown in this image:
What you’re doing is specifying a number format for positive numbers first, then negative numbers and then zero values, each separated by a semi-colon.
Copy in the symbols from step 1 (you’ll have to do this separately for each one).
Use the square brackets to specify the color you want e.g. [color50] for green.
(Yes, it’s an Excel article, but the rules are the same.)
9. Format like a pro!
After all that effort to tease out the real stories hidden in your data, and make them accessible in charts and tables, it’s worth a little effort to spruce up the final version. Consider some of these ideas:
Change the color of charts in your Google Sheets dashboard to match your brand
Give all the tables a consistent format, e.g. light gray borders, a bold header row with white text and alternate gray/white shaded rows
Remove the gridlines. Find this option in the View menu: View > Gridlines
Add your logo to the top of the dashboard
Hide all working tabs except the dashboard tab (does not affect the functionality of the dashboard)
Use freeze panes, to lock specific rows or columns, so that if a user scrolls the header row(s) will be locked in place for example, and the title and user input options will always be visible. It’s found in the View menu: View > Freeze
View the dashboard in full screen mode
10. Share and publish your Google Sheets dashboard for the world to see
It’s quite likely you’ll want to share your dashboard with colleagues, clients and/or the world. There are a couple of ways of doing this.
Firstly, you can click the Share button in the top right corner of the screen, which opens up the sharing options pane:
From here, you can enter email addresses to share directly with colleagues, or you can grab the sharing url and email that to people you want to share with, or paste into social media channels.