Here is the recursive function in question, without the second function to append the rows (I really wanted 1 all inclusive function anyway): def triangle(n): Instead it returns a jumbled mess of a nested list completely filled with 1's. The desired output should be a list of lists where each internal list contains one row of the triangle. I even tried writing a separate function which iterates over the range of the input number and calls the recursive function with the iterated digit while appending the individual lines to list before returning that list. But several attempts to have it produce the entire triangle up to and including that row have failed. I have gotten to the point where I can get it to produce the individual row corresponding to the number passed in as an argument. If you right-click the link and open it in an Incognito window you’ll be able to see it.After completing an assignment to create pascal's triangle using an iterative function, I have attempted to recreate it using a recursive function. If you can’t access the template, it might be because of your organization’s Google Workspace settings.
Draw triangle free pascal free#
Sierpiński Triangle Templateįeel free to make a copy: File > Make a copy… Method 2: Color ScaleĪnd here’s a variation using color scales within conditional formatting to achieve a similar effect:īoth of these examples are available in the template below. Look closely and you can see me change the value in A1, which changes the values of the formulas and subsequently changes the formatting applied too. I created a rule for 2 as we did above, then replicate it for 3 but with a different color, then 4, then 5, etc. Here I set conditional formatting rules for each value up to 12, i.e. Either: i) set up a new rule for each number, or ii) use the color scales (easier method).
Draw triangle free pascal update#
To see the effects, you need to update the conditional formatting rules. Start with 2 as you set the Sheet up, but then feel free to experiment with different numbers. Then in cell A1 put the value to be used as the divisor.
Draw triangle free pascal mod#
To finish, you can also remove the gridlines from the menu: View > Show > Gridlinesīy changing the divisor number in the MOD formula, you can explore the fractal nature of the Sierpiński Triangle.įollow the same steps as above, but modify the formulas so that the divisor in the MOD function is $A$1 rather than 2. This tells your Sheet to hide any values in the cells, so the 1’s and 0’s don’t show.
Go to the menu: Format > Number > Custom number format We’ll use a custom number format to do this. orange.Īs a final step, let’s remove the numbers. Set the format rule to “ Is equal to” and a value of 1.Ĭhange the background color to something bold, e.g. Go to the menu: Format > Conditional formatting Highlight the 32 by 32 grid - the range B2:AG33 - and add conditional formatting. Next, highlight the formulas in cells B3:B33 and drag across the rows to column AG.įollowing these 6 steps, you should have a grid of 1’s and 0’s as follows: This is the value in the top left corner of the triangle. Next, highlight all your columns and reduce the width so they’re squares. The Sierpiński triangle is a modified version where a modulo 2 operation is performed after the addition.įirstly, add additional columns up to AH so that our drawing can be 32 cells wide by 32 cells tall. Pascal’s triangle is a triangle made up of numbers where each number is the sum of the two numbers above. However, we use a different method - Pascal’s triangle - to draw an approximation in Google Sheets. Repeat with each smaller triangle an infinite number of times. Start with an equilateral triangle, subdivide it into four smaller triangles and remove the central triangle. Perhaps the easiest method to visualize is the removing-triangles method. There are many different methods to construct the Sierpiński triangle. See Wikipedia for more on the Sierpiński triangle.
It has the property of being self-similar, meaning it looks the same at any magnification. It is named after the Polish mathematician Wacław Sierpiński and is also known as the Sierpiński gasket or Sierpiński sieve. 🔗 Get this example and others in the template at the bottom of this article. Graphically, we can draw an approximation of the Sierpiński triangle in Google Sheets:
The Sierpiński triangle is a fractal set in the shape of an equilateral triangle, divided into smaller triangles infinitely.
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