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Logarithmic spiral

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Doyle Spiral Circle Packing - Grasshopper - McNeel Forum

Greetings, I am trying to achieve what is known as Doyle Spiral packing (space filling) the mathematical equation to map the center points of the circle is complex, on researching i came across the mathematicians or…

Anna Eck
Anna Eck saved to doodle
Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Fibonacci spiral with illuminated mount                                                                                                                                                                                 More

Fibonacci spiral with illuminated mount (private collection) Mineral colours, gold and silver on paper and archival mount board. Dimensions: 49 cm X 38 cm.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

LucasVB (1ucasvb) auf Twitter: „You've seen logarithmic spirals, but here's the Spiral Logarithm! It has its radial distance to the origin equal to the (offset) logarithm of its arc-length: r = log(s+1). Pictured log base 2. I came up with this the other day, but didn't find it being constructed elsewhere. https://t.co/u3GQ3P9R4v“ / Twitter

You've seen logarithmic spirals, but here's the Spiral Logarithm! It has its radial distance to the origin equal to the (offset) logarithm of its arc-length: r = log(s+1). Pictured log base 2. I came up with this the other day, but didn't find it being constructed elsewhere.

Fibonacci Spiral - Golden Spiral Logarithmic spiral whose growth factor is φ, the golden ratio - gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.

Fibonacci Spiral - Golden Spiral Logarithmic spiral whose growth factor is φ, the golden ratio - gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.

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Short, easy-to-read paragraphs are followed by comprehension activities that require students to pay attention to details, understand the content, know word definitions, draw conclusions, and write complete-sentence answers. This program is ideal for: Special Education / Special Needs Struggling Learners Students-at-Risk Learning Disabled Remedial Education Differentiated Education 32 Pages

Short, easy-to-read paragraphs are followed by comprehension activities that require students to pay attention to details, understand the content, know word definitions, draw conclusions, and write complete-sentence answers. This program is ideal for: Special Education / Special Needs Struggling Learners Students-at-Risk Learning Disabled Remedial Education Differentiated Education 32 Pages