How do you read the --> in z-->z²+c

[Chillheimer]

Hi!
I'm making a short movie about fractals and have to read the m-set formula.
do you say z equals z²+c?
or does the arrow have its own word?
Thx in advance!

[claude]

"z equals z squared plus c" is wrong (it defines a quadratic equation with two solutions).

"z maps to z squared plus c" is probably what I would say, or modifying or leaving out the "maps" depending on context ("repeated iterations of the mapping 'z to z squared plus c'" could work), although the LaTeX symbol is slightly different: \mapsto, vs \to

alternatively subscripts with iteration can use an explicit equals:  "z n plus one equals z n squared plus c"

[kram1032]

"is mapped to" or "is replaced by" or "is substituted for"
The difference between

and

is that refers to the M-set at any given iteration step - it's valid for all of them, whereas talks about the limit set. Only in the limit of infinitely many iterations is it actually true that .

Although claude is right that usually would be considered a quadratic equation with two solutions. It only works as I described if you consider z to be the entire Julia- or Mandelbrot set, rather than a single point which only holds true for a few trivial cases (namely the above mentioned solutions of the quadratic equation).

[quaz0r]

all of that is rather awkward for casually speaking the words...  couldnt one say Zn+1 equals Zn^2 + c, or for that matter, just say z equals z^2 + c, the fact that you are referring to how each iteration is calculated either being implied or explicitly stated, as opposed to deffining a quadractic euqation (claude hasnt had his coffee yet)      i think the casual listener probably won't assume you are wrongly defining a quadratic equation and feel all horribly offended and led astray..

[kram1032]

In how far is saying "z maps to z squared plus c" any more or less awkward than saying "z equals z squared plus c" and how is it any more awkward than explicitly mentioning the iteration variable "z n plus one equals z n squared plus c"? Why mention variables that are only used internally for housekeeping? Explicitly mentioning the iteration variables is both awkward and ambiguous.
"z equals z squared plus c" will rarely but occasionally be ambiguous.
"z maps to z squared plus c" never is ambiguous.

[Chillheimer]

Thx guys, "maps to" is exactly what I was looking for.
Falls jemand die deutsche Übersetzung kennt, die wüsste ich auch gerne..

[hobold]

Thx guys, "maps to" is exactly what I was looking for.
Falls jemand die deutsche Übersetzung kennt, die wüsste ich auch gerne..

"z wird abgebildet auf z² + c"