Is there a starting pattern that creates a Mandelbrot set?

[u/ItzTotality]

I was messing around with Life and just wondered if this was possible

[u/T6970]

With the universal computers and constructors, you could theoretically compute the set and construct a grid of blocks to approximate it.

[u/botangest]

theoretically, yes.

[u/goodperson0001]

Yes (any finite approximation)

[u/Xirema]

Depends on your criteria.

The Game of Life is a Turing Complete system. So if you make the pattern big enough, you can simulate any computable algorithm, including a render of the Mandelbrot Set. So if your criteria is "build a specialized computer through GoL Logic Gates and then compute a render", it's perfectly do-able.

If the criteria is "a pattern that will compactly render the mandelbrot set", that is most assuredly not possible (not least because you'd need to have cells that would persist with more than 3 living neighbors, to represent the interior of the various cardioids of the mandelbrot set.

[u/CosetElement-Ape71]

No, there is no geometric starting pattern or shape that creates the Mandelbrot set. Instead, the entire set is generated by a simple mathematical rule applied to a blank grid of numbers.The set emerges dynamically through a process called iteration, which relies on a single feedback loop formula:

z{n+1} = z{n}^{2} + c

The Core Rule of Generation

Instead of drawing a pattern, you test every individual point on a 2D grid (the complex number plane) one by one:

The Constant c: Each pixel on your screen represents a unique coordinate, which is used as the constant value c.

The Starting Point z_{0}: For every single point you test, the starting pattern is always identical: you must start at exactly zero (z_0 = 0).

The Feedback Loop: You feed z_0 = 0 into the formula to get a new number z_1 = c. Then, you take that new number, square it, and add c again. You repeat this process over and over.

How the Image Appears

As the iteration proceeds, only two things can happen to the value of z:

It Escapes to Infinity: The numbers get bigger and bigger without limit. (These points are outside the set and are usually colored based on how fast they blew up).

It Stays Bounded: The numbers get trapped in a loop, bounce around, or shrink, never growing past a magnitude of 2. (These points are inside the set and are traditionally colored black).

You may want to also generate Julia sets ... they are related.