First off, here is a gif that will show you exactly what the Mandelbrot set is all about, and how stunning it is:

As you can see, the set repeats variations of itself infinitely. This is a very fancy gif. Why stop here? Let’s find out the math behind this incredible discovery.

The Mandelbrot Set

The Mandelbrot set is a very famous assortment of complex numbers named after mathematician Benoit Mandelbrot. Wikipedia’s definition of the Mandelbrot set is: 

“The Mandelbrot set is the set of complex numbers for which the function  F_c (z) = z² does not diverge when iterated from z=0“

When first glancing at this, unless you have a solid background in mathematics, this may seem like a group of letters and numbers glued together at random…

However, there is no need to panic, as we’ll go through each definition thoroughly. By the end of this article, you’ll be able to interpret Wikipedia’s definition effortlessly. 

Complex Numbers

First of all, we must take into consideration a number line: the visual representation of… numbers on a line:

We are representing “natural numbers“. These include positive numbers, negative numbers, decimals, and so on. 

On the line, we can also position things like squared roots, for example, the squared root of 1, which is 1, and so on. 

However, what we cannot position on the line is the squared root of negative numbers. This is because when you square negative numbers, the final result will always be positive. 

For example:

2^2 = 4

-2^2 = 4

This means the squared root of, for example, -1 is unobtainable. However, mathematicians have established that the square root of -1 does exist, and its value is i.

The letter i stands for “imaginary” and its values are not included on the number line. However, if we draw a perpendicular axis things change.

Instead of a number line, we now have a complex number plane, which is the combination of natural and imaginary numbers. Every number on the number plane is technically the combination of a natural and imaginary number.

How do we know what numbers belong to the Mandelbrot set? Let’s figure out what functions are first.

Functions

A function is a relationship between two given numbers. Functions apply a predetermined set of rules to a set of numbers. Let’s take an example:

As you can see, we use x as a placeholder for any number. An input of 2 would result in an output of 4, an input of 4 would result in an output of 16, and so on. 

Verifying if a number belongs to the set

To verify if a number belongs to the Mandelbrot set, we use the function we mentioned at the beginning of the article:

First, we assign z a value of 0 (that’s the rule for the function to correctly work), next, we take any complex number (c), for example, 1, and add it to z. We then take the result and insert it into the function, iterating it. If the function keeps returning non-consistent values, then we know the complex number we picked does not belong to the Mandelbrot value.

However, with certain numbers such as -1 and start iterating them, we will notice a certain pattern repeating itself: the results of the function will always be either 0 or 1. This means -1 is part of the Mandelbrot set

Conclusion

The Mandelbrot set is one of modern mathematic’s greatest discoveries. It is amazing to think about how much it took us to find it.

We had to invent computers, graphical processing software, and so on. This shows just how little we know about our universe, and how much more there is to discover

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As fun of an idea it may sound, scientists and researchers are looking into transforming cloning humans into a reality. Let’s dig deeper.

What is Cloning?

Cloning is the process of producing genetically identical individuals of an organism. Mother nature has already figured out a way to do it, with many species of trees and plants. This is done through something called asexual reproduction, where offsprings arise from a single organism. 

A question someone may ask is: “Why don’t all living things just clone themselves, instead of having trouble finding partners? Wouldn’t it be more efficient?” If you think about it, evolution is based on the mixing of two different genetic heritages, where the stronger characteristics survive. Without normal sexual reproduction, there would be no evolution, therefore, no progress.

Why should we clone ourselves?

Leaving aside the comfort aspect, which is not achievable due to ethical problems, clones could be used in long term missions in space, once we will have the capabilities of building powerful and long-lasting spaceships. Other than that, the other possible uses of cloning are full of controversies and ethical issues, so we haven’t come to a conclusion

Uses of cloning

Cloning has excessive usages in various fields, such as medicine, agriculture, biology, etc. 

For instance, cloning could be used to clone endangered species, organ transplants, and possibly, immortality. The question is if you were cloned, would it really be you?

How cloning works

In 1996, cloning was revolutionized, when Ian Wilmut, at the Roslin Institute in Scotland, successfully cloned a sheep, named Dolly. Dolly was, in fact, the first animal to have ever been cloned. 

Wilmut and his colleagues transplanted a nucleus from a mammary gland cell of a Finn Dorsett sheep into the enucleated egg of a Scottish blackface ewe. The nucleus-egg combination was stimulated with electricity to fuse the two and to stimulate cell division. The new cell divided and was placed in the uterus of a blackface ewe to develop. Dolly was born months later.

Dolly was shown to be genetically identical to the Finn Dorsett mammary cells and not to the blackface ewe, which clearly demonstrated that she was a successful clone (it took 276 attempts before the experiment was successful). Dolly has since grown and reproduced, a not-so-typical “and they lived happily ever after” scenario, but still valid.

Conclusion

Cloning will probably help us reach some state of immortality in the future, however, ethically speaking, machines and IA are, in our opinion, a better option.

Sources: wikipedia.com, britannica.com, learn.genetics.utah.ed, digitaltrends.com, science.howstuffworks.com

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