File:CollatzConjectureGraphMaxValues.jpg

English: The horizontal axis is a starting value n. The vertical axis represents the max value reached, following the collatz conjecture rule (n%2==0)?n/2:n*3+1, in the "chain" to one. Created using the following Mathematica code

Clear[maxList, nMax, n, nLooper]

n = 1;

maxList = {};




goTo = 10000;
While[n <= goTo,
 
 nLooper = n;
 nMax = n;
 While[nLooper > 1,
  If[nLooper > nMax, nMax = nLooper]
   
   If[Mod[nLooper, 2] == 0,
    nLooper = nLooper / 2,
    nLooper = nLooper * 3 + 1
    ]
  
  
  ];
 
 maxList = Join[maxList, {nMax}];
 n++;

 ]
ListPlot[maxList, AspectRatio -> 2] 

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