[1] actually, the plaine of complex numbers.

[2] a so called iteration formula.

[3] e.g. if the series "jumps in circles", i.e. reaches a point it has already visited. If this happens, the series can only repeat the same subsequence again and again.

[4] Z_i+1 = Z_i * Z_i + C, whith C being the starting point and Z starting with zero.

[5] picture 52, for example, has the forumla Z_i+1=(Abs2(Z_i)+P₁)^atan(Abs2(Z_i)+P₂)+C; with Abs2() being a function which assignes the real- and imaginary part its respecive absolute value, and P₁ and P₂ being constant complex numbers.

[6] actually rather "a structure".

[7] constructivism or platonism?

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