You can see the large lightest gray circle around the shape are the points that escaped in 1 iteration. This is repeated with smaller and smaller numbers on the complex plane. It's done a third time, all points that escaped are a new color. All points that escaped in 2 iterations are given a new color. The computer performs a second iteration. All points within this color "escaped" the set in 1 iteration of the equation. This is the key.Īfter a computer has performed the equation on all complex numbers within 2, we get a an area of the plane shaded a certain color. Therefore, results larger than 2 are ignored and seen as "escaping" the Mandelbrot set. Repeating the equation with each new result, substituting Z like before, will grow the results exponentially fast.Īs you saw earlier, the number 2 thrown into the equation grew to 146 in only 3 iterations. This is because once a result goes beyond 2, If we get a result that falls outside 2 on the plane we color it a certain color. When we plug in these weird ass complex numbers into the Z = Z² + C equation, we take the resulting complex number and plot it on the graph.
Now we get into the real meat of this whole thing. So it's represented with the symbol "i"Ī complex number can look something like this. There is technically no solution to the square root of a negative number. Since squaring neither a positive nor a negative number will result in a negative number,
If you hated math like me and forgot what an imaginary number is, it's the square root of a negative number. A complex number is the addition of a real number to an imaginary number. Now when we start to plug in complex numbers into the equation, thats when weird shit starts to happen. When you do this with simple numbers, like 2, the results are nothing out of the ordinary. We then take that result in substitute it back into the equation and repeat the process. Keeping C the same original number, and re performing the equation. Then we'll be substituting Z with the result we got, The entire thing revolves around this simple equation.īasically, we'll be starting by plugging in the same number into Z and C, performing the equation and getting a result.
It's not too complicated to understand with a bit of math knowledge, but it's a little difficult toĮxplain so I'm going to do my best to explain it as simple as possible. So you're probably asking how the hell we get this thing in the picture. I decided I'd make a thread to share with you, what is quite possibly, the biggest mind fuck ever. Thread about the mathematician Benoit Mandelbrot's death. I searched for a thread but only found some brief mentions of it in a I had no idea this thing existed until recently and decided to see if it'd had ever been discussed here. Let’s start with the definition: “The HFD is defined as the diameter of a circle that is centered on the unfocused star image in which half of the total star flux is inside the circle and half is outside.What the fuck is that thing you ask? Simply put, it's a shape produced by an equation that can be zoomed into infinitely and will grow and change infinitely more complex. The original paper from Larry Weber and Steve Bradley is available here. Another short definition of the HFD I found here. There is another article about the HFD available here. The main two arguments for using the HFD is robustness and less computational effort compared to the FWHM approach. It was invented by Larry Weber and Steve Brady. Another measure for the star focus is the Half Flux Diameter (HFD).
The magic circle of infinity series#
In Part 5 of my “Night sky image processing” Series I wrote about measuring the FWHM value of a star using curve fitting.
0 kommentar(er)
