Math Is Fun Forum

Mandelbrot's set is one of the most known fractals out there.
It really sticks out.

The set contains all complex numbers, which if infinitely raised to power of 2 and added the initial value to, don't blow up to infinity but converge to a value.
You can also create another fractal, or halo, around the set if you plot the last breakpoint value.

If you think that every function transforms 2D plane's every point, the act of complex exponentation will bend the straight lines invards infinitely. With negative values the numbers close to zero explode close to infinity and wise versa.

You can also create other fantastic fractals with similar equations, namely, {iterated = iterated ^ start + start}, {iterated = start ^ initerated}, {iterated = -iterated ^ iterated}, {iterated = sqrt(iterated)+initial}
just to name a few. With some of these the halos are more incredible than the actual set.

the point is that I will make an esoteric programming language myself to be actually used,

so the question is about "esoteric things" in general which can be used in such.
like chaotic logistic maps, unlambda calculus, arithmetic with n-dimensional branes.
"those things".

languages themselves could be nice but they are rarely other than hard to read.
if you know some which stand out I would really appreciate that

they are quite simple actually, in my opinion at least.

  int x = 1;  // regular integer

  int[] y;     // an integer array! it is still just an empty name...

  y = new int[5];   // we put a fresh array length of length 5 to it. think of box with exactly 5 slots for ints.

  y[0] = 11;    // we can access the 5 slots with "index". indexes start from zero. (so 0,1,2,3 and 4 are valid).

  y = new int[99]; // we erase the current array and create new one, as size cannot change in-between.

  for(int i=0; i<y.length; i++){  y[i] = i+1; }   // we put numbers 1-99 to the array.

  try{  y[100] = 0; } // watch here, we access 101th slot in the array, which does not exist.
  catch(IndexOutOfBoundsException){}   // an error will be raised. be careful with this.

  string[] z; // string array is as fine as any other...

  myObject[] mo;   // any obeject can form an array!

  bool[,] b = new bool[10,10] // a fancy, two-dimensional array! it works like other arrays, but you must give two indexes to access "a slot".

  bool[,,,] bbb = new bool[2,4,6,8]; // while this is legit, it may use lots of space.

  int[][] ii = new int[5][]; // an array of array of ints! box, which contains boxes, which contain ints.

  ii[0] = new int[4]   // a new box to a box.

  ii[0][0] // a number to box inside box.

arrays have also many useful built-in methods which you can search from the manual.