{"id":797,"date":"2017-09-04T21:22:04","date_gmt":"2017-09-05T01:22:04","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=797"},"modified":"2017-10-11T11:18:25","modified_gmt":"2017-10-11T15:18:25","slug":"sierpinski-triangle-3","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/04\/sierpinski-triangle-3\/","title":{"rendered":"Sierpinski Triangle"},"content":{"rendered":"

For my fractal, I have chosen the Sierpinski Triangle.<\/p>\n

According to a Wikipedia<\/a> article,\u00a0Wac\u0142aw Sierpi\u0144ski first\u00a0described his self named triangle in 1915; however, the same article also notes that this fractal can be seen in designs dating back to the thirteenth century.<\/p>\n

The article described this fractal as an attractive fixed set; unfortunately, I do not know exactly what that means. Luckily for me, the process for creating this fractal was fairly simple and I found it very interesting. The most interesting part about this fractal is that it is subdivided recursively. What this means is that, rather than parts being added to the original shape to make an intricate pattern, parts are removed. By first taking an equilateral triangle, dividing it into four smaller, equilateral triangles, and removing the one in the middle you have started the first phase of this fractal. As we remove more and more triangles, the shape becomes that much more complex. Not to mention that the number of subtractions that can be made are infinite. This can be slightly confusing to simply imagine, so below I have included a picture that shows what this fractal would look like in five phases:<\/p>\n

\"Image<\/p>\n

While doing my research, I also found a youtube video that demonstrates the infinite qualities of this fractal. While the account that posted this video concedes that this is no illusion, I found Illusiontube<\/a>‘s video very helpful when it came to visualizing the infinite:<\/p>\n