I am going to morph a circle into the Mandelbrot. Now I can make circles. And I can make Mandelbrot, how to combine them? is Mandelbrot born of a circle? Where do I experience evidence that Mandelbrot is coming from circle? Am I replacing circle with Mandelbrot? Do I need circle to make Mandelbrot? Will such act not produce a monstrosity that is neither circle nor brot? What will happen? Because I don’t remember using circle to draw a Mandelbrot pixel by pixel before, and I never remember circle being in the mathematics of the Mandelbrot, for they just draw in a linear pattern across the pixel grid. So I understand how to apply Mandelbrot to overlay a circle. but what of actually making the circle’(s) morph into the brot? any suggestions?

What could possibly be the science here? Have they attempted to make a mirror of a circle and then that mirror behaves differently on positive to negative and then moved the circle geometry to produce impossible positions? so is the Mandelbrot formula a mirror drawing a skewed circle? With different reflection behaviours on the poles?

I ran some late night tests trying to allow the values of a Mandelbrot effect the values of modified circle. But all it produced outside of infinite was a deep infinite space effect. And a smaller spiralinng worm hole type effect and at some higher levels planetoids looking well lit highly characteristic spheres. But it was not a true implement of mandel. In my C sharp Mandelbrot I have the sum of the Mandelbrot applying the complex multiply and a list collecting the complex multiply value for me so it can be referenced to talk about parameters. However to use it to specify the values of a circle is difficult. The Mandelbrot does indeed form from an oval morphed from a circle. But to get only the outline of the structure is difficult I suppose I could get the values of the black and count out from the central rows until we hit a non black cell and write that coord in data. And stop painting any on the row after this colour segment. Then I suppose I could have a mechanism to slap a Mandelbrot outline down. Hmm but what use is that.

So wait. Apparently all I need to do is morph the circle into an oval. And then blow it out to infinite a number of times. ? ! ? i have to mimic the morph of the oval that makes up the shell of the brot

After speculation and consideration and numerous geometry and tests I concluded that Mandelbrot himself, was trying to reflect a sunrise on a water surface, when he was offsetting his circle and distorting it for which to discover the Mandelbrot. I can morph circles into ovals but I can’t split the circle into a brot. I can take the Mandelbrot values, floats, and then I can apply a sign wave fluctuation to these floats before building the maindelbrot image. This causes micro movement of the brot extensions. The arms will sway to the fluctuations of the wave.

No, the Mandelbrot does not "come from a circle", even though it has some sub regions that are perfect circles. The usual circle you see from the first iteration comes from the fact what kind of limit / cut-off function you're using and most simply use the magnitude from the origin. It's common to use a cut-off radius of 2 since it's known that the whole mandelbrot set lies within that circle. Also any complex number that has a magnitude greater than 2 will blow up to infinite as you keep iterating. So once a value gets larger than that radius, we know it will tend to infinity and we know it is not in the set. There is not really an easy test to say for sure if a point is in the set or not. There are some boundaries where we know they are in the set for sure, but especially the "edge" of the set is blurry and there is no easy way to tell if a certain point is in the set or not. What are you actually on about? First of all, be more clear what you're talking about. The Mandelbrot set is a mathematical set which was named after Benoît Mandelbrot. He has not discovered it. He was (one of) the first to visualize it thanks to computer support. The mandelbrot set is just about a mathematical property of the Z = Z² + C function. This has absolutely nothing to do with art. After it was discovered, a lot artists jumped on the train because the infinite complexity is artistically pleasing. Though the set itself is a pure mathematical property. The mandelbrot set is essentially a map for Julia sets that are connected. I'm not sure what you're philosophizing here and I highly doubt this has much relevance on this forum. Just to make this clear: The mandelbrot set has an infinite complex border which is infinitely long which you can never accuratly and fully represent. All images we have are approximations. It's a bit like transcendental numbers like PI. You can never write down an accurate decimal expansion of the number. Also keep in mind the actual set is just the inside, the part that is usually the most boring part for most artists. The coloring of the outside is purely based on artistic choices and have absolutely nothing to do with the set itself.

I too don't understand this speculation. There's solid mathematics and science behind this and it's well documented in many mediums from Youtube videos to books aimed at both the novice all the way to advanced mathematicians. A good starter looking at the Mandlebrot: A good overview of stuff like bifurcations etc: TBH, I always found the concept of periodic doubling, one of the roots of chaos, more fascinating that anything else and its appearance in real world physical systems. You can have a lot of geeky fun with software experimenting with this.