Fractals

The definition of fractals is quite extensive, so I will reduce it to a short interpretation that they represent images, created from repetitive patterns, and their representation is calculated by applying certain mathematical equations. Since I make an Excel greeting card almost every year and create a “recipe for drawing a Christmas tree” I will not deviate from tradition. We will “draw” the Christmas tree with the help of one simple fractal.

When you abstract the look of the Christmas tree, it comes down to a multitude of small triangles. For that reason, we will use repeating patterns of triangles to show it.

The first row of the table represents the initial values, which can be ones or zeros. In the second row, we enter a formula that examines whether the sum of three cells in the row above: left, above, and to the right of the current cell position is equal to one. If yes, the result is number 1. If not, the result is zero. Reduce the width of the columns to resemble squares.

Copy the formula into the remaining cells where you want to repeat this pattern, but keep in mind not to use it in cells “on the edge” of the area because that’s where Excel will report the error. Since we want the tree to be symmetrical, it is best not to enter values ​​in the top row except for number 1 in the very center of the area.

The pattern is already slowly emerging. In order for the tree to take on a better shape, we will first replace all formulas with values, and then change the font of all cells to Windings. With the Replace option, all cells that contain 1 should be replaced with asterisks, and that contain 0 with an empty string. Center the values ​​in the cells horizontally and vertically.

Finally, remove the lines that separate the cells, change the background and text colors, and write messages to wish you a Merry Christmas and a Happy New Year. Nice, isn’t it?