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==Visualizations== <gallery mode=packed heights="250"> File:Collatz orbits of the all integers up to 1000.svg|Directed graph showing the orbits of the first 1000 numbers. File:CollatzConjectureGraphMaxValues.jpg|The {{mvar|x}} axis represents starting number, the {{mvar|y}} axis represents the highest number reached during the chain to 1. This plot shows a restricted {{mvar|y}} axis: some {{mvar|x}} values produce intermediates as high as {{val|2.7e7}} (for {{math|''x'' {{=}} 9663}}) File:Collatz-max.png|The same plot as the previous one but on log scale, so all {{mvar|y}} values are shown. The first thick line towards the middle of the plot corresponds to the tip at 27, which reaches a maximum at 9232. File:All Collatz sequences of a length inferior to 20.svg|The tree of all the numbers having fewer than 20 steps. File:Collatz Conjecture 100M.jpg|alt=Collatz Conjecture 100M|The number of iterations it takes to get to one for the first 100 million numbers. File:Collatz_conjecture_tree_visualization.png|Collatz conjecture paths for 5000 random starting points below 1 million. </gallery>
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