What fractals, Fibonacci, and the golden ratio have to do with cauliflower

Self-selected mutations during domestication drastically changed shape over time

Macro-photo of green Romanesco cauliflower showcases the vegetable's striking fractal pattern.

Enlarge / Macro-photo of green Romanesco cauliflower showcases the vegetable's striking fractal pattern. (credit: Cathy Scola / Getty Images)

It's long been observed that many plants produce leaves, shoots, or flowers in spiral patterns. Cauliflower provides a unique example of this phenomenon, because those spirals repeat at several different size scales—a hallmark of fractal geometry. This self-similarity is particularly notable in the Romanesco variety because of the distinctive conical shape of its florets. Now, a team of French scientists from the CNRS has identified the underlying mechanism that gives rise to this unusual pattern, according to a new paper published in Science.

Fractal geometry is the mathematical offspring of chaos theory; a fractal is the pattern left behind in the wave of chaotic activity. That single geometric pattern repeats thousands of times at different magnifications (self-similarity). For that reason, fractals are often likened to Russian nesting dolls. Many fractal patterns exist only in mathematical theory, but over the last few decades, scientists have found there are fractal aspects to many irregular yet patterned shapes in nature, such the branchings of rivers and trees—or the strange self-similar repeating buds that make up the Romanesco cauliflower.

Each bud is made up of a series of smaller buds, although the pattern doesn't continue down to infinitely smaller size scales, so it's only an approximate fractal. The branched tips, called meristems, make up a logarithmic spiral, and the number of spirals on the head of Romanesco cauliflower is a Fibonacci number, which in turn is related to what's known as the "golden ratio."

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Microsoft may offer 7 different versions of Windows 11 (Home, Pro, Education, Mixed Reality, etc)

Windows 10 comes in five different flavors: there are Windows 10 S, Home, Pro, Education, and Enterprise Editions. But it looks like Microsoft is going to shake things up a bit when Windows 11 launches later this year. According to a new entry on the …

Windows 10 comes in five different flavors: there are Windows 10 S, Home, Pro, Education, and Enterprise Editions. But it looks like Microsoft is going to shake things up a bit when Windows 11 launches later this year. According to a new entry on the Bluetooth SIG website, there may be as many as seven […]

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Crowdfunding: xScreen portable display turns the xBox Series S into a gaming laptop (sans the battery)

There’s no shortage of portable displays that you can plug into a laptop, tablet, smartphone, or other gear when you need some extra screen space on the go. And theoretically there’s nothing stopping you from plugging those screens into an…

There’s no shortage of portable displays that you can plug into a laptop, tablet, smartphone, or other gear when you need some extra screen space on the go. And theoretically there’s nothing stopping you from plugging those screens into an xBox or any other game console. But the new xScreen is a portable display designed just […]

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New Google Pay debit card lets you actually spend the money people send you

A virtual debit card lets you skip transferring money to a bank account.

Earlier this year, Google blew up the existing Google Pay and started over with a new codebase that had more restrictions and fewer features. Now, the company is finally starting to add features on top of this stripped-down service, starting with the return of a debit card. According to a new report from 9to5Google (Google does not seem to have a blog post about this yet), starting this week, US Android users can request a "Google Pay Balance Card" that will allow them to spend their Google Pay balance directly on purchases.

Besides the NFC tap-and-pay functionality, Google Pay also has a P2P payment that lets you exchange money with other people. The pool for sending and receiving this money is your Google Pay balance, and previously, the main way to spend this balance was to transfer it out of Google Pay and into a bank account (though it's also a payment method on the Play Store and Google hardware store). This worked fine, and if it was deposited directly to a bank account, there weren't any fees. It was just a few extra taps and took several days to transfer. The new Google Pay card is a virtual Visa debit card that you can set as an NFC card, so now spending that money a friend sent you is as easy (and presumably quick) as setting your Google Pay balance as your NFC card and tapping your phone against a store payment terminal.

During Google's turbulent NFC payment history—spanning 2011's Google Wallet, 2015's Android Pay, 2018's Google Pay, and 2021's big revamp—almost everything has been done before. This Google Pay Balance Card feels a lot like the Google Wallet Card (2013-2016), which also let you spend your P2P balance in stores. That was a physical piece of plastic, though, and it didn't work over NFC. The Google Pay Balance Card is NFC-only and, despite the name, is not a physical card.

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Google Pixel 5a hits the FCC ahead of launch

Device makers don’t typically like to talk about products that haven’t been officially announced yet. But Google made an exception in April when it confirmed that a Pixel 5a was on the way by responding to rumors that the unannounced phone…

Device makers don’t typically like to talk about products that haven’t been officially announced yet. But Google made an exception in April when it confirmed that a Pixel 5a was on the way by responding to rumors that the unannounced phone had been cancelled. Google says the phone will be available in the US and […]

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Google “bought off Samsung” to limit app store competition, 36 states allege

“Google has taken steps to close the ecosystem from competition.”

Google “bought off Samsung” to limit app store competition, 36 states allege

Enlarge (credit: Andri Koolme / Flickr)

Yesterday, dozens of state attorneys general sued Google on antitrust grounds, alleging that the company worked to “preemptively quash” competing app stores (most notably the Samsung Galaxy Store) and maintain its monopoly on Android app distribution.

The lawsuit alleges that Google engaged in a range of anticompetitive practices, including offering large app developers profit-sharing agreements in exchange for exclusivity, creating unnecessary hurdles for sideloading, and attempting “to buy off Samsung to limit competition from the Samsung Galaxy app store.”

Google says the lawsuit is “meritless.” “It’s strange that a group of state attorneys general chose to file a lawsuit attacking a system that provides more openness and choice than others,” Wilson White, Google’s senior director of public policy, wrote in a blog post. 

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IPTV Operator Jailed For 16 Months For Selling & Watching Pirate Streams

A UK man has been sentenced to 16 months in prison for operating a pirate IPTV service. Paul Faulkner appeared before Liverpool Crown Court after pleading guilty to multiple copyright infringement and fraud offenses. According to the Premier League, Faulkner was also found guilty of watching his own service, an offense which netted him four months in prison.

From: TF, for the latest news on copyright battles, piracy and more.

Anoyone running a significant pirate IPTV operation in the UK, especially one that supplies sports content, runs the risk of being targeted by the Premier League and anti-piracy partners Federation Against Copyright Theft (FACT).

The pair have been involved in a number of criminal prosecutions of illicit TV suppliers over the years and today brings news of yet another conviction.

Joint Investigation

The target in this matter was a man called Paul Faulkner. He was reportedly the operator of TV Solutions, a pirate streaming service that offered illegal access to sports and entertainment content, including live Premier League matches and Sky channels.

This resulted in a joint investigation by the Premier League and FACT, which determined that Faulkner was selling access to his service on social media platforms and using the money generated as a second source of income. The Premier League then brought a private criminal prosecution to bring Faulkner before the courts.

Faulkner Pleads Guilty and is Sentenced

According to the Premier League, Faulkner pleaded guilty to multiple copyright infringement and fraud offenses and eventually appeared in front of Liverpool Crown Court on Tuesday.

He was jailed for a total of 16 months, not only for supplying the service to customers but also for watching it himself.

“Mr Faulkner pleaded guilty to both the unlawful supply of content and his own use of the service to view content he should have been paying to watch,” the Premier League says.

“The judge recognized that Faulkner’s use of the unauthorized service was a distinct crime in itself. This was reflected in him receiving a separate sentence of four months’ imprisonment for using the service.”

Also of interest is the Premier League’s reference to VPNs in respect of this case.

“Despite the defendant selling access to his service on social media platforms as a secondary source of income, the judge made it clear this case was a sophisticated fraud carried out over a significant period of time, made more serious by the involvement of Virtual Private Networks (VPNs),” the football group notes.

No Surprise That Watching Streams and VPNs Are Highlighted

While tracking down and prosecuting IPTV providers is an important part of the Premier League’s strategy, it also faces problems when it comes to deterring the general public from buying these packages and being able to successfully use them on match days.

Until 2017, it was widely believed that simply watching pirated streams wasn’t an offense in the EU. Indeed, in 2016 the EU Commission claimed that the act wasn’t illegal, a position supported by Trading Standards in the UK. However, the ‘Filmspeler’ decision removed all doubt, concluding that selling boxes and streaming pirated content amounted to copyright infringement.

The mention that Faulkner received a four-month sentence for viewing illegal streams on his own service is meant as a clear signal to pirate IPTV buyers that they too could receive a similar sentence. While that could and should act as a deterrent, it should be noted that the Court may have taken Faulkner’s wider offending into consideration when handing down what appears to be a very stiff sentence.

The other issue faced by the Premier League is the effectiveness of its ISP blocking program. Just last month the football group obtained yet another blocking injunction in Ireland, one that’s even more stringent than the last. However, this can be circumvented in seconds with the use of a VPN.

The exact circumstances of Faulkner’s use or promotion of VPNs aren’t made clear by the Premier League but by mentioning the technology as an aggravating factor in his case, there’s clearly an effort to portray these circumvention devices as problematic, not only for IPTV providers but users too.

From: TF, for the latest news on copyright battles, piracy and more.

Qualcomm’s first self-branded smartphone is an enthusiast-class flagship (that’s made by Asus)

The company that makes the processors that power many of the world’s smartphones is now launching its own phone. The new Qualcomm Smartphone for Snapdragon Insiders is designed and manufactured by Asus, but it’s designed to show off the be…

The company that makes the processors that power many of the world’s smartphones is now launching its own phone. The new Qualcomm Smartphone for Snapdragon Insiders is designed and manufactured by Asus, but it’s designed to show off the best of Qualcomm’s technologies and the phone is marketed at members of the company’s Snapdragon Insiders community. […]

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