Lone wolf or lone actor attacks are a particular kind of mass murder, committed in public settings by individuals who plan and commit these violent acts on their own. In the United States, such attacks are usually committed with firearms. In other countries, knives are sometimes used to commit mass stabbings.
Lone actor attacks are a social construct, rather than a legal term, and have become the subject of academic research. The academic definition of lone actor mass shootings means they occur in a public setting and excludes the killing of multiple people if those deaths occur during the commission of other crimes, such as bank robberies or during gang warfare. The definition also excludes killings such as familicide where the perpetrator kills the rest of of their family in a private setting. Criminologist, Grant Duwe, has identified 845 mass shootings in the United States between 1976 and 2018. However, only 158 of these met the criteria for a lone actor shooting which occurred in a public setting.
The descriptor 'lone wolf' is derived from the notion of a lone wolf, a pack animal which has left, or been excluded from its pack. This particular term is more likely to be used by American law enforcement than by academics who study this phenomenon. Studies have found that some lone wolf attacks are committed because of personal grievances and a desire for revenge, while others are acts of terrorism, intended to induce fear and influence the way people think.
The term lone actor or lone wolf is not a legal term or a social science concept. It is an ill-defined and academically contested construct, manufactured by the media and by radical political actors.
Academic studies tend to distinguish between lone actors and lone actor terrorists. This is because broadly speaking, two types of Lone Actor attacks have been identified: those that are ideologically driven - politically or religiously - and intended to create fear and influence public opinion; and shootings committed by individuals with a grievance against an institution such as their school or workplace.  In the United States, the perpetrators generally use guns, whereas in other countries where the public have less access to guns (such as China), knives may be used to commit mass stabbings.
In the United States in particular, lone actor attacks are associated with mass shootings in which multiple people are shot - although the definition of a mass shooting is also contested. Different sources describe the minimum number of victims as between three and five, with most authorities describing four as the minimum. Some sources include injured victims in the total while other definitions specify the victims must be dead in order to be counted.
The definition also requires mass shootings associated with lone actors to have occurred in a public situation. Familicides where one member of a family kills all other members in the family home are not considered as lone actor shootings.
United States law enforcement agencies have paid particular attention to the terrorist-type lone wolf attacks and popularized the term "lone wolf terrorism". Lone wolf terrorists may sympathize with and consider themselves part of larger groups, but they are usually not active participants. The links between lone wolves and actual terrorist groups tend to be informal and conducted online. These individuals tend to become radicalized online and through media outlets.
There have been cases of terrorist attacks conducted by individuals which were later found to have been directed remotely by terrorist organisations. Thus they were technically not lone wolves.
The era of anarchist terrorism, 1878-1934, should be considered the classic age of ''lone wolf'' or leaderless terrorism. Before this period, nineteenth century terrorists and assassins, such as the Italian nationalist Felice Orsini, the Irish Fenians, and the Russian populists, had constructed elaborate, sometimes inter-national, conspiracies to carry out their violent deeds. By contrast, after the late 1870s the anarchists rejected authoritarian, centralized control over acts of planned violence as well as over anything else. Of the total number of violent anarchist incidents, which runs into the hundreds--possibly thousands if we include the quasi civil wars in Russia after the 1905 Revolution and in Barcelona in 1919-23--less than a handful were the product of large-scale conspiracies. All the rest were the deeds of lone individuals or of very small groups without command structures or leaders. 
Since 1940, there have only been around 100 successful lone wolf attacks in the United States. The number of attacks is increasing, however, and has grown each year since 2000. As compared to those on the far right, lone wolf attackers who become inspired by al-Qaeda and ISIS tend to be younger and better educated. According to studies, lone wolves have more in common with mass murderers than they do with members of the organized terrorist groups that often inspire them. The FBI and San Diego Police's investigation into the activities of a self-professed white supremacist, Alex Curtis, was named Operation Lone Wolf, "largely due to Curtis' encouragement of other white supremacists to follow what Curtis refers to as 'lone wolf' activism".
While the lone wolf acts to advance the ideological or philosophical beliefs of an extremist group, they act on their own, without any outside command or direction. The lone wolf's tactics and methods are conceived and directed solely on their own; in many cases, such as the tactics described by Curtis, the lone wolf never has personal contact with the group they identify with. As such, it is considerably more difficult for counter-terrorism officials to gather intelligence on lone wolves, since they may not come into contact with routine counter-terrorist surveillance. A 2013 analysis by Sarah Teich, a research assistant at the International Institute for Counter-Terrorism, found five emerging trends in Islamist lone wolf terrorism in North America and western Europe between 1990 and 2013:
In the United States, lone wolves may present a greater threat than organized groups, and lone wolf attackers have not been limited to Muslims.
Some groups actively advocate lone wolf actions. Anti-abortion militant terrorist group the Army of God uses "leaderless resistance" as its organizing principle. According to The New York Times, in news analysis of the Boston Marathon bombing, the Al-Qaeda activist Samir Khan, publishing in Inspire, advocated individual terrorist actions directed at Americans and published detailed recipes online.
Compared to the general population, lone wolf terrorists are significantly more likely to have been diagnosed with a mental illness, although it is not an accurate profiler. Studies have found that roughly a third of lone wolf terrorists have been diagnosed at some point in their life with a mental illness. This puts lone wolves as being 13.5 times more likely to suffer from a mental illness than a member of an organized terrorist group, such as al-Qaeda or ISIS. Environmental factors such as relationships with those belonging to a terrorist group, social isolation, and various stressors mediate the relationship between mental illness and lone wolf terrorism.
Mental health challenges are thought to make some individuals among the many who suffer from certain "psychological disturbances", vulnerable to being inspired by extremist ideologies to commit acts of lone wolf terrorism. An alternative explanation is that terrorist groups reject those with mental illnesses as they pose a security risk, creating a selection bias.
The terms "narratives of insecurity", "scripted violence" and "stochastic terrorism" are linked in an indirect chain cause-effect relationship. Public use of "narratives of insecurity"[This quote needs a citation] can prompt the rhetoric of "scripted violence" which can result in an act of "stochastic terrorism".
"Mass violence is not the product of religion or culture. It is born of narratives of insecurity", writes professor Abdelwahab El-Affendi. It is the "effect of narrative framing" that "holds the key to understanding instances of mass violence".[This quote needs a citation] He has collected a set of essays in the book Genocidal Nightmares: Narratives of Insecurity and the Logic of Mass Atrocities.
Responding to a question about a series of mass shootings in the United States that involved two young men who carried out the mass shootings on August 3, 2019 in El Paso, Texas and August 4, 2019 in Dayton, Ohio, Abdelwahab El-Affendi said these perpetrators of violence "were acting in a different movie from the one we are all watching. In their story, they were not opening fire on 'innocent people', but heroically responding to 'an existential threat'."
The phrase "scripted violence" has been used in social science since at least 2002.
Author David Neiwert, who wrote the book Alt-America, told Salon interviewer Chauncey Devega:
Scripted violence is where a person who has a national platform describes the kind of violence that they want to be carried out. He identifies the targets and leaves it up to the listeners to carry out this violence. It is a form of terrorism. It is an act and a social phenomenon where there is an agreement to inflict massive violence on a whole segment of society. Again, this violence is led by people in high-profile positions in the media and the government. They're the ones who do the scripting, and it is ordinary people who carry it out. Think of it like Charles Manson and his followers. Manson wrote the script; he didn't commit any of those murders. He just had his followers carry them out.
The first mention of the term "stochastic terrorism" appears to be in a 2002 article written by Gordon Woo entitled "Quantitative Terrorism Risk Assessment" in the Journal of Risk Finance. The term is used to suggest that a quantifiable relationship may exist between seemingly random acts of terror and their intended goal of "perpetuating a reign of fear" via a manipulation of mass media and its capacity for "instant global news communication". For example, careful timing and placement of just a few moderately explosive devices could have the same intended effect as numerous random attacks or the use of more powerful explosives if they were shrewdly devised to elicit the maximum response from media organizations. Thus, it was theorized by Dr Woo that "the absolute number of attacks within a year, i.e. the rhythm of terror, might ultimately be determined as much by publicity goals and the political anniversary calendar as by the size of the terrorist ranks".
A derivation of Dr Woo's stochastic terrorism model was proffered by an anonymous blogger posting on Daily Kos in 2011 to describe public speech that can be expected to incite terrorism without a direct organizational link between the inciter and the perpetrator. The term "stochastic" is used in this instance to describe the random, probabilistic nature of its effect: whether or not an attack actually takes place. And, although the actual perpetrator of a planned attack and its timing is not under the control of the stochastic terrorist, their actions nevertheless serve to increase the probability that a terrorist attack will occur. The stochastic terrorist in this context does not direct the actions of any particular individual or members of a group. Rather, the stochastic terrorist gives voice to a specific ideology via mass media with the aim of optimizing its dissemination.
It is by dint of this ideology that the stochastic terrorist is alleged to randomly incite individuals predisposed to acts of violence. And it is because the stochastic terrorist does not target and incite individual perpetrators of terror with their message that the perpetrator may be labeled a lone wolf by law enforcement while the inciter avoids legal culpability. The term has mostly been applied to domestic American incidents of violence.
In their 2017 book Age of Lone Wolf Terrorism, criminologist Mark S. Hamm and sociologist Ramón Spaaij discuss stochastic terrorism as a form of "indirect enabling" of terrorists. They write that "stochastic terrorism is the method of international recruitment used by ISIS", and they refer to Anwar al-Awlaki and Alex Jones as stochastic terrorists.:157
Hamm and Spaaij discuss two instances of violence. In the 2010 Oakland freeway shootout, Byron Williams was said to be en route to offices of the American Civil Liberties Union and the Tides Foundation, planning to commit mass murder, "indirectly enabled by the conspiracy theories" of Glenn Beck and Alex Jones. As a left-wing example, they cite the 2012 shooting incident at the headquarters of the Family Research Council.
The stochastic terrorism model is a stochastic process, a random model of those terror attacks intended by the random nature of their timing and targets to excite a generalized fear. Nonetheless, lone wolf terrorists are "indirectly enabled by the conspiracy theories" circulated in the mass media, especially by high status political or religious leaders.