.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/consensus/pow/plot_02_hashcash.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_consensus_pow_plot_02_hashcash.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_consensus_pow_plot_02_hashcash.py:


Hashcash: proof of work you can verify in one hash (Back 1997)
==============================================================

With d leading zero bits, a uniform hash succeeds with probability 2**(-d).
The expected search is 2**d trials, but any one run can finish much earlier
or later. Nonce search changes a commitment without changing the payload.

What to look for
----------------

Compare measured mining attempts with the average predicted by difficulty. Individual
searches fluctuate: the average is not a deadline.

Read cells in order. An ``assert`` that produces no output has passed.
The final exercise asks you to change an input and explain the result.

The history behind this experiment: :doc:`/history/consensus_breakthroughs`.
See :doc:`/exercises/consensus` for a worked solution to the exercise.

.. GENERATED FROM PYTHON SOURCE LINES 23-40

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    import blockchainkit as bk

    difficulties = list(range(2, 10))
    samples = []
    for difficulty in difficulties:
        attempts = []
        for trial in range(20):
            block = bk.structures.Block(difficulty=difficulty, timestamp=trial)
            result = bk.consensus.mine(block, max_attempts=100_000)
            assert bk.consensus.valid_pow(result.block)
            attempts.append(result.attempts)
        samples.append(attempts)
    print("Measured means:", [round(float(np.mean(row)), 1) for row in samples])





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Measured means: [4.2, 12.8, 10.9, 19.0, 68.3, 113.1, 196.8, 558.5]




.. GENERATED FROM PYTHON SOURCE LINES 41-73

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    means = np.mean(samples, axis=1)
    axes[0].plot(difficulties, means, "o-", label="20 searches per difficulty")
    axes[0].plot(
        difficulties,
        [bk.consensus.expected_trials(d) for d in difficulties],
        "--",
        label="Expected 2^d",
    )
    axes[0].set(
        yscale="log",
        xlabel="Leading zero bits d",
        ylabel="Hash trials",
        title="Mining cost grows exponentially",
    )
    axes[0].legend(fontsize=8)
    for fraction in (0.1, 0.25, 0.4):
        deficits = list(range(1, 11))
        axes[1].plot(
            deficits,
            [bk.consensus.eventual_catch_up(fraction, z) for z in deficits],
            label=f"q={fraction}",
        )
    axes[1].set(
        yscale="log",
        xlabel="Current block deficit",
        ylabel="Eventual catch-up probability",
        title="Ideal random-walk model",
    )
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/consensus/pow/images/sphx_glr_plot_02_hashcash_001.png
   :alt: Mining cost grows exponentially, Ideal random-walk model
   :srcset: /api/gallery/consensus/pow/images/sphx_glr_plot_02_hashcash_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 74-79

Exercise
--------
Repeat with more trials and compare means and medians. The right plot
assumes independent block discoveries and an infinite horizon; it is not
Nakamoto's Poisson confirmation calculation and omits propagation effects.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.584 seconds)


.. _sphx_glr_download_api_gallery_consensus_pow_plot_02_hashcash.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/consensus/pow/plot_02_hashcash.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_hashcash.ipynb <plot_02_hashcash.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_hashcash.py <plot_02_hashcash.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_hashcash.zip <plot_02_hashcash.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_