How do you do the simple "check" to rid the wrong answers? And why exactly did you specify v(t)>0?

How do you do the simple "check" to rid the wrong answers? And why exactly did you specify v(t)>0?

I have a 2x2 matrix. If my first eigenvalue is real and >0 and my second is real and <0, and my Trace^2-4*det < 0 at the fixed point (theta=0.6087705581, v=.9057326898), how does this imply that it is a SPIRAL SINK??? I am looking at this webpage: http://www.math.sunysb.edu/~scott/Book331/Fixed_Point_Analysis.html and I see that its a spiral sink iff lamba1 and lamba2 are complex and <0 but here, lamba1 is and greater than zero. Can someone explain why this is?

I knew I needed the 120 degree turn but I kept using 80 as my TurtleAngle. I understand why 40 works as the angle now! Using the same method with a different angle I made the smoother one :) Thanks!!

I knew I needed the 120 degree turn but I kept using 80 as my TurtleAngle. I understand why 40 works as the angle now! Using the same method with a different angle I made the smoother one :) Thanks!!

Yes!! :):) thankyou

I understand that if you set the SetTurtleAngle(>60) it will get spikier and if you do SetTurtleAngle(<60) it will get smoother but then my snowflake either breaks apart or overlaps. Should I be adding more recursions when I lower the Turtleangle or something? Not quite sure what I'm missing here. I also tried messing around with the growing "G" and shrinking "S" but I dont think that either are necessary to use to make it spikier or smoother.

Yes!! :):) thankyou

I understand that if you set the SetTurtleAngle(>60) it will get spikier and if you do SetTurtleAngle(<60) it will get smoother but then my snowflake either breaks apart or overlaps. Should I be adding more recursions when I lower the Turtleangle or something? Not quite sure what I'm missing here. I also tried messing around with the growing "G" and shrinking "S" but I dont think that either are necessary to use to make it spikier or smoother.

@Carl Love I'm stuck. How can I change my coding to have the shape repeat itself of 3 sides of an equalaterial triangle to form the snowflake?

@Carl Love Im using a txt file I found online titled sutherland. I think I might have figured it out or gotten to a good start though!!!

ReadFromWeb:=proc(URL::string, {printfile::truefalse:=false})
 local n,m, status, webfile, headers;
 status,webfile,headers:=HTTP[Get](URL):
 if ( HTTP[Code](status) <> "OK") then
     error(HTTP[Code](status),URL);
 fi;
 # now read the web page
 n:=0:
 while (n < length(webfile)) do
   m:=n;
   parse(webfile,statement,lastread='n', offset=n);
   if (printfile) then printf("%s",webfile[m+1..n]); fi;
 od:
end:

ReadFromWeb("http://www.math.sunysb.edu/~scott/mat331.spr13/problems/turtle.txt");

Koch:=proc(n::posint)    
  if (n=1) then return("F"); fi;
 ## now n>1
  return( cat( " ",Koch(n-1), "L", Koch(n-1), "RR", Koch(n-1), "L", Koch(n-1), " ","RR", " ",Koch(n-1), "L", Koch(n-1), "RR", Koch(n-1), "L", Koch(n-1), " ","RR", " ",Koch(n-1), "L", Koch(n-1), "RR", Koch(n-1), "L", Koch(n-1), " ","RR"));
end:

SetTurtleAngle(60): TurtleCmd(Koch(2));

This is a great help!!! I have a few questions to start though. Here, what do a and b represent and when you write the command (r1,c1):=to_row_col(a), are you substituting the value of 'a' into 'n' in the to_row_col expression above? Also, if I had (r1,c1)=(2,3) [2nd row,3rd column] then how would I find to_row_col(a)? I'm not sure if I made my question clear or not lol

This is a great help!!! I have a few questions to start though. Here, what do a and b represent and when you write the command (r1,c1):=to_row_col(a), are you substituting the value of 'a' into 'n' in the to_row_col expression above? Also, if I had (r1,c1)=(2,3) [2nd row,3rd column] then how would I find to_row_col(a)? I'm not sure if I made my question clear or not lol

Yes this is what I was looking for. But do you mind explaining the WFI and WFO coding a little more? And that works for small messages but what about a larger one like this: I see it stops after 6 "blocks".

T:=Select(IsUpper,UpperCase("
I can show you the world
Shining, shimmering, splendid
Tell me, princess, now when did
You last let your heart decide?

I can open your eyes
Take you wonder by wonder
Over, sideways and under
On a magic carpet ride

A whole new world
A new fantastic point of view
No one to tell us no
Or where to go
Or say we're only dreaming

A whole new world
A dazzling place I never knew
But when I'm way up here
It's crystal clear
that now I'm in a whole new world with you"));

                      >"ICANSHOWYOUTHEWORLDSHININGSHIMMERINGSPLENDIDTELLMEPRINCESSNOWWH\

  ENDIDYOULASTLETYOURHEARTDECIDEICANOPENYOUREYESTAKEYOUWONDERBYW\

  ONDEROVERSIDEWAYSANDUNDERONAMAGICCARPETRIDEAWHOLENEWWORLDANEWF\

  ANTASTICPOINTOFVIEWNOONETOTELLUSNOORWHERETOGOORSAYWEREONLYDREA\

  MINGAWHOLENEWWORLDADAZZLINGPLACEINEVERKNEWBUTWHENIMWAYUPHEREIT\

  SCRYSTALCLEARTHATNOWIMINAWHOLENEWWORLDWITHYOU"


sprintf(cat(WFO, cat(" ",WFO) $ words-1), sscanf(T, cat(WFI $ words))[]);
             "ICANS HOWYO UTHEW ORLDS HININ GSHIM"

Yes this is what I was looking for. But do you mind explaining the WFI and WFO coding a little more? And that works for small messages but what about a larger one like this: I see it stops after 6 "blocks".

T:=Select(IsUpper,UpperCase("
I can show you the world
Shining, shimmering, splendid
Tell me, princess, now when did
You last let your heart decide?

I can open your eyes
Take you wonder by wonder
Over, sideways and under
On a magic carpet ride

A whole new world
A new fantastic point of view
No one to tell us no
Or where to go
Or say we're only dreaming

A whole new world
A dazzling place I never knew
But when I'm way up here
It's crystal clear
that now I'm in a whole new world with you"));

                      >"ICANSHOWYOUTHEWORLDSHININGSHIMMERINGSPLENDIDTELLMEPRINCESSNOWWH\

  ENDIDYOULASTLETYOURHEARTDECIDEICANOPENYOUREYESTAKEYOUWONDERBYW\

  ONDEROVERSIDEWAYSANDUNDERONAMAGICCARPETRIDEAWHOLENEWWORLDANEWF\

  ANTASTICPOINTOFVIEWNOONETOTELLUSNOORWHERETOGOORSAYWEREONLYDREA\

  MINGAWHOLENEWWORLDADAZZLINGPLACEINEVERKNEWBUTWHENIMWAYUPHEREIT\

  SCRYSTALCLEARTHATNOWIMINAWHOLENEWWORLDWITHYOU"


sprintf(cat(WFO, cat(" ",WFO) $ words-1), sscanf(T, cat(WFI $ words))[]);
             "ICANS HOWYO UTHEW ORLDS HININ GSHIM"

I'm curious as to how to set up/format the printf command for this given problem. Any ideas?

I'm curious as to how to set up/format the printf command for this given problem. Any ideas?