Paulo F Cunha

re Riemann's zeta function

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

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  • Prompt: Imagine you have a list of natural numbers (1, 2, 3, 4, ...). Riemann's zeta function takes a number 's' and sums the reciprocals of all the numbers in that list raised to the power of 's'. For example, zeta(2) = 1/1^2 + 1/2^2 + 1/3^2 + ... (sum of reciprocals of squares of natural numbers). This function is interesting because it helps solve many problems related to prime numbers, which are the building blocks of all natural numbers. However, the zeta function is not defined for all values of 's'. It gets a bit tricky at 's' = 1. The trickiness at s = 1 in the Riemann zeta function can be visualized by imagining a teeter-totter: Think about the sum for zeta(2) again: 1/1^2 + 1/2^2 + 1/3^2 + .... Each term gets smaller and smaller as you go further down the list. This makes the sum well-behaved and eventually converges to a specific value. But now, imagine s = 1. The sum becomes 1/1 + 1/2 + 1/3 + .... Here, each term is either 1 or bigger than 1. It's like putting only heavy weights on one side of the teeter-totter. The sum keeps getting bigger and bigger, never settling on a specific value. Mathematicians call this situation "divergence." There are ways to define the zeta function for other values of 's' even though the simple sum diverges at 1. It's like using advanced techniques to balance the teeter-totter so it makes sense even with those heavy weights. But understanding that initial imbalance at s = 1 is the first hurdle.
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simplicial symmetric sphere spectrum

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

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  • Prompt: The concept of a simplicial symmetric sphere spectrum into simple terms: Spheres of differing dimensions. A 0-sphere is just two points, a 1-sphere is a circle, a 2-sphere is the surface of a ball, and so on. A “spectrum” is like a sequence of these spheres, where each sphere is connected to the next one in a way that helps us study shapes and spaces in a stable manner. The “sphere spectrum” is a particular sequence that starts with the 0-sphere, and includes all higher-dimensional spheres. The "symmetric" part means we're keeping track of how these spheres can be rearranged or swapped around; important because it allows us to do more operations with our spectrum. “Simplicial” refers to a way of building complex shapes from simple pieces, like Legos. Meaning that we're using a particular mathematical structure to describe how our spheres connect. Thus a “simplicial symmetric sphere spectrum” is a sequence of spheres of increasing dimensions, built such that we can swap them around and perform various operations on them; this structure is useful for studying shapes and spaces in a way that's more flexible and powerful than just looking at individual spheres. Thus the “simplicial symmetric sphere spectrum” is a powerful mathematical concept that bridges the gap between geometry and abstract algebra. It's a sequence of spheres of increasing dimensions, connected in a way that allows mathematicians to perform complex operations across dimensions. This is crucial in topology, the study of shapes and spaces. The "symmetric" aspect allows for rearrangements of spheres, enabling operations like addition and multiplication of entire spaces. The "simplicial" component allows building complex shapes from simple elements – the “Lego block” approach, making the concept computationally manageable, and also connecting it to fields like computer graphics and data science. Thus mathematicians gain insights into the very fabric of reality as we u
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SN 56:48 Chiggaḷa Sutta

• Model: AIVision

• Size: 2048 X 2048 (4.19 MP)

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  • Prompt: A sea-turtle rises from oceanic depths in golden hour, breaking the surface with its head at the very center of an elliptical wooden yoke floating upon the vast open sea. From a neuronally-mediated probabilistic spatio-temporal past the echo of the original words being spoken in Pali, long-unheard by mortal beings: “Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind from the east would push it west; a wind from the west would push it east. A wind from the north would push it south; a wind from the south would push it north. And suppose a blind sea turtle were there. It would come to the surface once every one hundred years. Now what do you think? Would that blind sea turtle, coming to the surface once every one hundred years, stick his neck into the yoke with a single hole?” “It would be a sheer coincidence, lord, that the blind sea turtle, coming to the surface once every one hundred years, would stick his neck into the yoke with a single hole.” “It’s likewise a sheer coincidence that one obtains the human state. It’s likewise a sheer coincidence that a Tathāgata, worthy & rightly self-awakened, arises in the world. It’s likewise a sheer coincidence that a Dhamma & Vinaya expounded by a Tathāgata appears in the world. Now, this human state has been obtained. A Tathāgata, worthy & rightly self-awakened, has arisen in the world. A Dhamma & Vinaya expounded by a Tathāgata appears in the world. “Therefore your duty is the contemplation, ‘This is stress … This is the origination of stress … This is the cessation of stress.’ Your duty is the contemplation, ‘This is the path of practice leading to the cessation of stress."
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La Révolution surréaliste in Arles

• Model: Artistic 2

• Size: 1925 X 2597 (5.00 MP)

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  • Prompt: Arles Amphitheater. 17th century, city by the sea, by Pieter Bruegel & Iwona Lifsches & Kev Munday
  • Using base image: Yes (Effect strength - 50%)
  • Base image resolution: Default
  • Upscale & Enhance: 5

Watercolor classic in Vienne 1

• Model: DigitalDaVinci

• Size: 1941 X 2576 (5.00 MP)

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  • Prompt: Cathédrale Saint-Maurice. Architectural drawing: sketch..Construction details. "border town 1880":watercolor, charcoal, ink, by Pablo Picasso, Wlad Safronow
  • Using base image: Yes (Effect strength - 64%)
  • Base image resolution: Default
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Mirò's springs in Nantes 1

• Model: Artistic 2

• Size: 1941 X 2576 (5.00 MP)

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  • Prompt: Architecture, leaves, flowers, styles Miro and Kandinsky
  • Using base image: Yes (Effect strength - 60%)
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The golden age of Baroque in Rome 1

• Model: Artistic

• Size: 1941 X 2576 (5.00 MP)

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  • Prompt: Church of Sant'Agnese in Agone in Rome.17th century, city by the sea, by Pieter Bruegel & Iwona Lifsches & Kev Munday
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  • Aspect Ratio: landscape

A Midsummer Night's Dream in Ferrara 1

• Model: Photonic

• Size: 1932 X 2588 (5.00 MP)

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  • Prompt: Este Castle in Ferrara. Architectural drawing sketch and Construction details. 3D, Zentangle, elegant, surreal, beautiful acrylic art, watercolor patchwork, Picasso, Wassily Kandinsky, spirals and intricate patterns, contour lines. Very colorful. Gustav Klimt style.
  • Using base image: Yes (Effect strength - 54%)
  • Base image resolution: Default
  • Upscale & Enhance: 5

Lucy in the Sky .... in Bourges 1

• Model: Photonic

• Size: 1919 X 2606 (5.00 MP)

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  • Prompt: Bourges cathedral. Architectural drawing sketch and Construction details. 3D, Zentangle, elegant, surreal, beautiful acrylic art, watercolor patchwork, Picasso, Wassily Kandinsky, spirals and intricate patterns, contour lines. Very colorful. Gustav Klimt style.
  • Using base image: Yes (Effect strength - 54%)
  • Base image resolution: Default
  • Upscale & Enhance: 5

The Da Vinci Codex in Rome 1

• Model: Artistic

• Size: 1941 X 2576 (5.00 MP)

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  • Prompt: Castel Sant'Angelo in Rome. Architectural drawing sketch and Construction details. Codex Atlanticus, A Leonardo Da Vince drawing plan for Renaissance architecture in details, sketch on ink over an old paper, A. DÜRER and Rembrandt and Escher drawing style. [Must have 4 wings]
  • Using base image: Yes (Effect strength - 60%)
  • Base image resolution: Default
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Waiting for Godot in Milan 1

• Model: DreamForge

• Size: 1941 X 2576 (5.00 MP)

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  • Prompt: Zen philosophers in an empty room. Alien visitors from Sirius, all sitting around waiting for GODOT. a ladder. Written on a school blackboard: THIS IS NOT ART, an enigmatic southern farmhouse with a Joseph Cornell attic and Bourges Cathedral in the background
  • Using base image: Yes (Effect strength - 60%)
  • Base image resolution: Default
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Colors of Italy in Naples 1

• Model: Photonic

• Size: 1941 X 2576 (5.00 MP)

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  • Prompt: Chambord castle. Architectural drawing sketch and Construction details. 3D, Zentangle, elegant, surreal, beautiful acrylic art, watercolor patchwork, Picasso, Wassily Kandinsky, spirals and intricate patterns, contour lines. Very colorful. Gustav Klimt style.
  • Using base image: Yes (Effect strength - 54%)
  • Base image resolution: Default
  • Upscale & Enhance: 5