Shows the <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity" class="extiw" title="en:Kolmogorov complexity">Kolmogorov complexity</a> <i>K</i>(<i>s</i>) <span style="background:transparent;color:#c00000;font-weight:400;" title="transparent">(red)</span>, and two computable lower bound functions, <code>prog1(s)</code> <span style="background:transparent;color:#00c000;font-weight:400;" title="transparent">(green)</span>, <code>prog2(s)</code> <span style="background:transparent;color:#0000c0;font-weight:400;" title="transparent">(blue)</span>. The horizontal axis (<a href="https://en.wikipedia.org/wiki/logarithmic_scale" class="extiw" title="en:logarithmic scale">logarithmic scale</a>) enumerates all <a href="https://en.wikipedia.org/wiki/string_(computer_science)" class="extiw" title="en:string (computer science)">strings</a> <i>s</i>, ordered by length; the vertical axis (<a href="https://en.wikipedia.org/wiki/linear_scale" class="extiw" title="en:linear scale">linear scale</a>) measures string length in <a href="https://en.wikipedia.org/wiki/bit" class="extiw" title="en:bit">bits</a>; the depth axis lines up the shown functions. Most strings are incompressible, i.e. their Kolmogorov complexity exceeds their length by a constant amount. Nine compressible strings are shown in the picture, appearing as almost vertical slopes. Due to <a href="https://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin's_incompleteness_theorem" class="extiw" title="en:Kolmogorov complexity">Chaitin's incompleteness theorem</a>, the output of any program computing a lower bound of the Kolmogorov complexity cannot exceed some fixed limit, which is independent of the input string <i>s</i>.
<a href="//commons.wikimedia.org/wiki/User:Jochen_Burghardt" title="User:Jochen Burghardt">Jochen Burghardt</a>
CC BY-SA 4.0
<span class="int-own-work" lang="en">Own work</span>