Thomson atomic model (1903)
The William Thomson (1903) model of atomic formation of structures, according to which non-living structures, e.g. crystals, are able to form via "fortuitous concourse of atoms", whereas anything "living", e.g. sprig of moss, microbe, or animal, being the handiwork of god and his miracles. [2]
In theories, fortuitous concourse of atoms, a terminological forerunner, in some sense, to the late 20th century "blind, random, chance, accident" model of mutation-based evolution, tends to generally refer to a non-divine model of plant, animal, and human formation according to pre-Cicero Greek atomic theory models.

Overview
The notion of things coming into being via a "fortuitous" concourse of atoms, supposedly originated in the Greek writings of Epicurus; possibly associated, in namesake, influence, or etymology, with the Greek goddess Fortuna (Ѻ), goddess of fate, chance, and luck.

In c.1700, the phrase "fortuitous concourse of atoms" was making the rounds among the English writers:

“A wonder it must be that there should be any man found so stupid as to persuade himself that this most beautiful world could be produced by the fortuitous concourse of atoms.”
John Ray (c.1700) (Ѻ)

“Philosophers say, that man is a microcosm, or little world, resembling in miniature every part of the great; and, in my opinion, the body natural may be compared to the body politic; and if this be so how can the Epicurean's opinion be true, that the universe was formed by a fortuitous concourse of atoms; which I will no more believe, than that the accidental jumbling of the letters of the alphabet could fall by chance [see: typing monkeys] into a most ingenious and learned treatise of philosophy. Risum tincatis amici? [hor] This false opinion must needs create many more; it is like an error in the first concoction, which cannot be corrected in the second; the foundation is weak, and whatever superstructure you raise upon it, must of necessity fall to the ground. Thus men are led from one error to another, until with Ixion they embrace a cloud instead of Juno; or, like the dog in the fable, lose the substance in gaping at the shadow: For such opinions cannot cohere; but like the iron and clay in the toes of Nebuchadnezzar's image, must separate and break in pieces. I have read in a certain author, that Alexander wept, because he had no more worlds to conquer; which he needed not have done, if the fortuitous concourse of atoms could create one; but this is an opinion fitter for that many headed beast the vulgar to entertain, than for so wise a man as Epicurus; the corrupt part of his sect only borrowed his name, as the monkey did the cat's claw to draw the chestnut out of the fire.”
Jonathan Swift (c.1720), “A Critical Essay on the Faculties of the Mind” (Ѻ)

In 1770, Baron d’Holbach clarified what correctly is meant by the term as follows:

“In seeing the world, we acknowledge a material cause of those phenomena which take place in it; and this cause is nature, of whom the energy is shown to those who study her. Let us not be told, that, according to this hypothesis, we attribute every thing to a ‘blind cause’, to the ‘fortuitous concurrence of atoms’; to ‘chance’. We only call those blind causes, of which we know not the combination, the power, and the laws. We call fortuitous, those effects of which we are ignorant of the causes, and which our ignorance and inexperience prevent us from foreseeing. We attribute to chance, all those effects of which we do not see the necessary connection with their causes. Nature is NOT a blind cause; she does NOT act by chance; NOTHING that she does would ever be fortuitous to him who should know her mode of acting, her resources, and her course. Every thing which she produces is necessary, and is never more than a consequence of her fixed and constant laws; every thing in her is connected by invisible bands (see: bond), and all those effects which we see flow necessarily from their causes, whether we know them or not.”
Baron d’Holbach (1770), The System of Nature (pg. 234)

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Quotes
The following are related quotes:

“My task has been rigorously confined to what, humanly speaking, we may call the ‘fortuitous concourse of atoms’, in the preparation of the earth as an abode fitted for life. Mathematics and dynamics fail us when we contemplate the earth, fitted for life but lifeless, and try to imagine the commencement of life upon it. This certainly did not take place by any action of chemistry, or electricity, or crystalline grouping of molecules under the influence of force, or by any possible kind of fortuitous concourse of atoms. We must pause, face to face with the mystery and miracle of creation of living creatures.”
William Thomson (1897), “The Age of the Earth as an Abode Fitted for Life” [1]

Cicero denied that [living things] could have come into existence by a fortuitous concourse of atoms. Was there anything so absurd as to believe that a number of atoms by falling together of their own accord could make a crystal, a sprig of moss, a microbe, a living animal? People thought that, given millions of years, these might come to pass, but they could not think that a million of millions of years could give them unaided a beautiful world like ours. They had a spiritual influence, and in science a knowledge that there was that influence in the world around them. He admired the healthy, breezy atmosphere of free thought in professor [John] Henslow's (Ѻ) lecture. Let no one be afraid of true freedom. They could be free in their thoughts, in their criticisms, and with freedom of thought they were bound to come to the conclusion that science was not antagonistic to religion but a help for religion.”
William Thomson (1903), show of thanks statement during the George Henslow “Christian Apologetics” lecture; note: Thomson recanted on this (see: Thomson on religion), in respect to crystals, two days later [2]

“Thus we can reconcile the philosophical position of our time with the words of the apostle; for the ‘higher pantheism’ [Tennyson] agrees with him in asserting the existence of the eternal ‘in whom we live and move and have our being.’ Science, conceiving of the universe as the manifestation of an immanent god, can only endorse these words. Goethe's name for the cosmos, which the fool in his folly was pleased to call a ‘fortuitous concourse of atoms,’ is this—‘the living garment of god’.”
Caleb Saleeby (1904), “The Living Garment of God” [3]

References
1. (a) Thomson, William. (1897). “The Age of the Earth as an Abode Fitted for Life” (Ѻ), Annual Address of the Victoria Institute (with additions written at various times from Jun 1897 to May 1898, in: Philosophical Magazine, 5(47):66-90, 1899.
(b) Smith, Crosbie and Wise, Norton. (1989). Energy and Empire: a Biographical Study of Lord Kelvin (pg. 612). Cambridge University Press.
(b) Kelvin’s quotes on science and religion? (2009) – Yahoo Answers.
2. (a) Thomson, William. (1903). “On Religion and Science”, praise commentary of George Henslow’s (Ѻ), lecture on Christian Apologetics, Botanical Theater, University College.
(b) Thomson, William. (1903). “On Religion and Science”, in: London Times, May 2.
(c) Walsh, James J. (1908). “Lord Kelvin” (Ѻ), Catholic World (quote, pgs. 758-59), 86:757-68.
3. Saleeby, Caleb. (1904). “The Living Garment of God”, in: The Cycle of Life According to Modern Science: Being a Series of Essays Designed to Bring Science Home to Men’s Business and Bosoms (pg. 343). Harper & Brothers.

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