Distribution of nonces and hashes: Difference between revisions
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→Distribution of Nonces: added more explanation about why the nonce distribution is skewed toward lower nonce values |
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[[ | Here we analyze the [[nonce]] values and [[hash|hashes]] for all the valid blocks in the [[blockchain]]:<ref>https://bitcoin.stackexchange.com/q/36414/4334</ref> | ||
====Nonces vs Hashes (y-axis logarithmic, x-axis linear) | ==Time Evolution== | ||
===Nonces vs Hashes (y-axis logarithmic, x-axis linear)=== | |||
This plot readily shows that the distribution of [[nonce|nonces]] that produce valid [[hash|hashes]] is uniform.<br>[[File:Nonces vs Hashes.png|verba alia]] | This plot readily shows that the distribution of [[nonce|nonces]] that produce valid [[hash|hashes]] is uniform.<br>[[File:Nonces vs Hashes.png|verba alia]] | ||
===Nonces vs Hashes (log-log scale)=== | |||
[[File:Nonces vs Hashes (log-log scale).png|Nonces vs Hashes (log-log scale)]] | [[File:Nonces vs Hashes (log-log scale).png|Nonces vs Hashes (log-log scale)]] | ||
In the animated version of this last plot,<ref>cf. [https://i.imgur.com/W08tgUr.gif animated version (incremental, 1k blocks shown at a time)] or [https://i.imgur.com/3LkacLD.gif animated version (cumulative)]</ref> you can really visualize the change in the [[difficulty]] and even see where the [[difficulty]] was decreased. | In the animated version of this last plot,<ref>cf. [https://i.imgur.com/W08tgUr.gif animated version (incremental, 1k blocks shown at a time)] or [https://i.imgur.com/3LkacLD.gif animated version (cumulative)]</ref> you can really visualize the change in the [[difficulty]] and even see where the [[difficulty]] was decreased. | ||
==Histograms== | |||
===Distribution of Nonces=== | |||
The nonces found are skewed toward 0 because this is a [[Wikipedia:Selection_bias|selection effect]]: most everyone starts searching for nonces starting at 0, so the lower nonces are found first, even though there may be also higher nonces that could produce a winning block:<br>[[File:Nonces Histogram.png|histogram of nonces]] | |||
===Distribution of Hashes=== | |||
Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):<br>[[File:Hashes Histogram.png|histogram of hashes]] | |||
===2-D Distribution of Nonces & Hashes=== | |||
2-D histogram of hashes and nonces (logarithmic color scale):<br>[[File:Density Plot (log colorscale).png|Density Plot (log colorscale)]] | |||
<br> | |||
This also illustrates very well that the distribution of nonces is uniform. | |||
==References== | ==References== | ||
Latest revision as of 02:08, 14 March 2015
Here we analyze the nonce values and hashes for all the valid blocks in the blockchain:[1]
Time Evolution
Nonces vs Hashes (y-axis logarithmic, x-axis linear)
This plot readily shows that the distribution of nonces that produce valid hashes is uniform.
Nonces vs Hashes (log-log scale)
.png)
In the animated version of this last plot,[2] you can really visualize the change in the difficulty and even see where the difficulty was decreased.
Histograms
Distribution of Nonces
The nonces found are skewed toward 0 because this is a selection effect: most everyone starts searching for nonces starting at 0, so the lower nonces are found first, even though there may be also higher nonces that could produce a winning block:
Distribution of Hashes
Although the distribution of hashes is not uniform, this does not matter; all that matters is that the distribution of nonces is uniform (which they are, minus the selection effect of starting at 0):
2-D Distribution of Nonces & Hashes
2-D histogram of hashes and nonces (logarithmic color scale):.png)
This also illustrates very well that the distribution of nonces is uniform.
References
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