Title: How do you read the --> in z-->z²+c
Post by: Chillheimer on April 25, 2016, 12:34:33 PM
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!
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!
Title: Re: How do you read the --> in z-->z²+c
Post by: claude on April 25, 2016, 01:06:00 PM
"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"
"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:
alternatively subscripts with iteration can use an explicit equals: "z n plus one equals z n squared plus c"
Title: Re: How do you read the --> in z-->z²+c
Post by: kram1032 on April 25, 2016, 01:21:15 PM
"is mapped to" or "is replaced by" or "is substituted for"
The difference between
 \ \ \ z \to z^2+c)
and
 \ \ \ z=z^2+c)
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).
The difference between
and
is that
Although claude is right that usually
Title: Re: How do you read the --> in z-->z²+c
Post by: quaz0r on April 25, 2016, 01:34:43 PM
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..
Title: Re: How do you read the --> in z-->z²+c
Post by: kram1032 on April 25, 2016, 01:49:10 PM
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.
"z equals z squared plus c" will rarely but occasionally be ambiguous.
"z maps to z squared plus c" never is ambiguous.
Title: Re: How do you read the --> in z-->z²+c
Post by: Chillheimer on April 26, 2016, 10:45:35 AM
Thx guys, "maps to" is exactly what I was looking for.
Falls jemand die deutsche Übersetzung kennt, die wüsste ich auch gerne..
Falls jemand die deutsche Übersetzung kennt, die wüsste ich auch gerne..
Title: Re: How do you read the --> in z-->z²+c
Post by: hobold on April 26, 2016, 11:34:43 AM
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"Falls jemand die deutsche Übersetzung kennt, die wüsste ich auch gerne..