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https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/230af167-7482-46c2-9e53-e62d805e2655/10_B10_160x160_20250826_224223_bjn.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1757822887482-7VW82MZRRS4SUH8RWOT3/Screenshot+2025-09-10+at+2.45.34%E2%80%AFPM.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1746379506330-MTIPK8RRQ7QS1ZTQVG6F/Screenshot%2B2024-12-30%2Bat%2B12.22.44%25E2%2580%25AFAM.jpg Home A computer-generated fractal image showing a detailed colorful pattern with a central black circle surrounded by intricate green, blue, and yellow shapes on the right and grainy, pixelated pattern on the left, with the left titled 'Source Image' and the right titled 'Droste Effect Image with 80 Columns'. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/5924103b-94e7-4ee7-9234-28e5921cbd20/Screenshot+2024-12-04+at+7.01.06%E2%80%AFPM.png Home Abstract digital artwork featuring a vibrant rainbow gradient on the left, transitioning into complex, concentric, wavy patterns in pink, purple, and gray hues on the right. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/f456c3f9-1604-4c62-9edb-3ca6daac4d83/Screenshot+2024-10-04+at+10.29.20%E2%80%AFPM.png Home Blurred multicolored gradient background with shades of blue, green, pink, purple, and yellow. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/b272cd8f-2824-4e58-b4f2-909139c4b6a2/Screenshot+2024-10-04+at+9.14.08%E2%80%AFPM.png Home A fractal graph with branches in red, purple, and blue colors, showing a recursive pattern. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1752165500848-UHDNF5BOPTVTR2T2OWRX/KoalaXing_BJN.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/40ad76d5-f809-4f1d-ace0-f3d664e8ead6/1+Colors.png Home Series of optical illusions showing spinning spiral patterns in yellow and blue with varying number of colors from 8 to 1. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/b2931254-2129-4288-af39-03dcdea3dba8/Screenshot+2024-12-19+at+4.15.17%E2%80%AFPM.png Home An abstract colorful pattern with overlapping red, yellow, and black rings over a background of red, green, and yellow squares with a blurred, textured appearance. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/70a2ada8-dec4-4271-85b6-f55c3ddf7479/julia_set_esque_B10_250x250_20250826_193529_bjn.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/b0357304-4e7d-4fde-9778-9b6380086a68/mandelbrot_b_2_iter_500_20240806_053420.png Home A digital fractal with black circles and intricate patterns in red, black, and green, creating a swirling abstract design. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/5f6fba12-a23d-4afb-8b67-ee782ee28443/Screenshot+2024-12-07+at+10.27.53%E2%80%AFAM.png Home Abstract digital artwork with multicolored geometric shapes, including red, purple, blue, green, and pink sections, with wave-like patterns and sharp edges. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1e20fb76-0e26-4164-aed4-4fed6b3566a5/Screenshot+2024-12-03+at+10.24.10%E2%80%AFPM+of+screenshot+_+BJN+TuringBrock.png Home A digital abstract pattern with multicolored concentric circles and wavy lines creating an optical illusion. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/caca614e-276f-4c05-bc9f-3ca9b01c93cb/tan_z__Regular.png Home Colorful fractal pattern with a gradient green background and rainbow-colored circular shapes aligned in a row. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/b6005fc7-807d-4eae-a4f2-86a89d802e51/Screenshot+2024-12-29+at+10.24.28%E2%80%AFPM.png Home Digital circuit pattern with colorful grid and lines in pink, green, blue, yellow, and orange https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/71f6f546-e445-4373-8377-22ceb0bae47c/boolean_function_table_exhaustive.png Home A colorful matrix heat map titled 'Boolean Function Transformation Table with Redundant Patterns Combined'. The table contains many columns of multicolored vertical bars and rows labeled from 1 to F in the Y-axis, with each cell displaying binary data, numbers, and letters. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/fab5d586-e900-4f41-af28-6958c6a8f069/RGB_HilbertCurveDiagnol.png Home A colorful RGB space with a Hilbert curve path overlay, displaying a gradient of colors from black, purple, pink, red, green, cyan, and white. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/506e4e4b-a1a6-4345-b396-71f1aec3c93c/Continuous+Wave+Evolution+for+%24a%5En Home A contour plot illustrating the evolution of a continuous wave for a complex number n with real part ranging from -10 to 10, and imaginary part from -150 to 150. The plot shows color gradients representing the gradient of n, with a color bar on the right indicating the magnitude from 0 to 1. The title indicates the wave is for a power of -1 with a base of 2. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/80489f62-3976-4ee2-a663-80251627fb69/NewBrockAlgebraGroup_1.png Home A grid of 15 subplots displaying color-coded complex functions: standard functions, Brock algebra variations with and without history for sine, cosine, exponential, logarithm, hyperbolic tangent, and hyperbolic sine, plus their difference maps. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/eb5983a0-c4f1-408a-a472-d851a9547124/Screenshot+2024-10-27+at+12.36.34%E2%80%AFPM.png Home A graph titled 'Reduced Numerators and Prime Factor Dip Factors for n = 1 to 1000' displays a large collection of colored vertical bars representing data points. The x-axis is labeled 'n (Sequence Index)' and ranges from 0 to 900, while the y-axis is labeled 'Reduced Numerator Values.' A color bar on the right corresponds to different dip factors, with levels from 1 to 8. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/6c12d6b1-94ca-45ac-bac1-83c24625ce9e/RGB%2C+Sinusoidal%2C+Radial%2C+Checkerboard.png Home A comparison of different gradient and checkerboard patterns with labels for each pattern, including sinusoidal, radial, and checkerboard styles in various color channels. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/23e5972b-4caa-4ee9-88c6-97f84e237267/HEIF+Image+2.jpeg Home Two side-by-side graphs illustrating complex numbers. The left graph displays colorful horizontal stripes representing the imaginary part, with the real part on the x-axis ranging from -10 to 10. The right graph shows a scatter plot of points with varying colors, indicating regions of the complex plane divided by the real and imaginary parts from -10 to 10, labeled with mathematical functions involving Brock Algebra. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/64ad8ed4-ad7f-4510-9f70-0394bda42b35/Brock+Algebra+Function+Visualization.png Home Colorful visual representation of Brock algebra function with real part on the x-axis and imaginary part on the y-axis, showcasing complex plane patterns with various color gradients. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/31787630-4903-4a31-9df1-9c895eecb0c1/Base-n+Representation2.png Home Scatter plots comparing three data representations: factorial in blue, primordial in green, and base-n in red, with the x-axis labeled 'Number' and the y-axis labeled 'Sum of Digits'. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/0e033990-82ae-40e0-b490-75237746b0b2/Screenshot+2024-10-05+at+3.54.01%E2%80%AFPM.png Home A barcode with black and white vertical lines, some containing noise or static texture. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/a9cf790a-2344-4ac4-83e5-4ea4aff1263b/Droste+Effect+Image+with+120+Columns+%28Simplified+Matching+with+Resizing%29.png Home A colorful digital art scene on the left side with various geometric shapes, spheres, cubes, and arches in bright colors, set against a gradient background. The right side displays a pixelated, simplified version of the same scene, using a grid of colored squares. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/7b2510ad-1a04-469e-8319-9ea3db753d97/Screenshot+2024-12-21+at+8.35.20%E2%80%AFPM.png Home A chart illustrating color channel permutations across RGB, HSV, and CMY color models, with gradients showing different color combinations and transitions. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/86e0f6a3-68a2-49ea-aadf-0da4eae6df27/Comprehensive+Polyhedra+Transformation+Graph.png Home A complex graph showing various 3D polyhedra and their relationships, including transformations like truncation, duality, and expansion. The nodes are colored to represent different types of polyhedra, such as pyramids, prisms, and cuboctahedra. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/dadf7710-3b6f-4e3d-a688-13953b082b53/Celestial+Distances+in+Astronomical+Units+%28AU%29.png Home Bar chart showing celestial distances in astronomical units (AU) from Sun to planets and Moon, with categories for Sun, Mercury, Venus, Earth, Moon, Mars, Jupiter, Saturn, Uranus, Neptune. The chart includes legend for distance types: Current Distance, Half-Orbit Forward, Half-Orbit Backward, Perihelion, Aphelion. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e20bb475-fa85-4d73-bd20-26cdb6c68dfe/All+18+Functions+with+Corrected+Lower+Humps+and+Inversions+2.png Home A complex graph displaying 18 mathematical functions, including sine, cosine, tangent, and others, with corrected lower humps and inversions, plotted over theta (radians) on the x-axis and function values on the y-axis, with a legend on the right indicating each function by color and line style. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/3ef814ee-9f4d-4b78-8572-883528c915d0/Comparison+of+Collatz+Sequences+with+Different+Factors+2.png Home Line graph comparing Collatz sequences with different factors. The x-axis shows steps from 0 to 1000, and the y-axis shows a logarithmic scale of values from 10^50 to 10^120. Multiple colored lines represent sequences with varied odd bases, powers, and moduli, illustrating how values decrease over steps. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/abc22c7c-eee3-415c-8122-cdf4d7b8bd31/Transformation+Path+Visualization+of+Hex+Values.png Home Line graph titled 'Transformation Path Visualization of Hex Values' showing the transformation of hexadecimal values over operation steps. Multiple colored lines represent different initial hex values, with a legend on the right listing hex values from 0x0 to 0xF. The x-axis includes steps labeled 'Start', '0', '<<', '>>', '!', '<<', and '>>', while the y-axis displays the hex value progress from 0 to 15 (0x0 to 0xF). The graph contains various data points connected by lines with labels indicating the hex value at each step. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/50b855c8-20c2-4860-a22a-9b4fdfd202c9/Matplotlib+Chart.png Home A chart titled 'Planetary Properties: Gravity, Size, and Orbital Motion' displays the gravity in meters per second squared, the radius in thousands of kilometers, and the orbital speed in kilometers per second of the Sun and planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and the Moon. The Sun has the highest gravity and radius, with the Moon having the lowest gravity and orbital speed. A red dashed line shows the free-fall acceleration toward the Sun for each celestial body. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/5f06066a-fcbf-4119-ad59-1d31a09e7a58/New+Weighted+Reviews+Needed+%28True+Ranking+Considered%29%3A+Scenario+5.png Home A set of eight charts showing review score distributions and the impact of additional reviews on product ratings across four different scenarios. The charts are organized in two columns, with the left side displaying review score distributions and the right side illustrating how new reviews affect the weighted average rating needed for true ranking considerations. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/b07405e2-24f3-4dd7-b236-a94ca17e5ab0/page_01.png Home A scientific comparison chart displaying various graphs of algebraic functions involving sine, cosine, hyperbolic sine, and hyperbolic cosine, each with regular, Brock algebra, and overlay difference visualizations. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/35ab23fd-a61c-4e50-92a9-cfd6bf1dafb1/All+Cones+Missing+%28Grayscale%2C+Corrected%29.png Home Color spectrum with different cones missing and corrected. Top: normal vision spectrum. Second: red cone missing. Third: green cone missing. Fourth: blue cone missing. Bottom: all cones missing in grayscale. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/8cbed861-3087-4461-8f43-3a31be741099/_grid_ImageGallery_20250419_182809.png Home Abstract digital pattern with colorful grid-like geometric shapes and diagonal lines. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e4771700-a97b-4fea-b8ea-895c77992840/BJN_Screenshot+2024-12-29+at+6.30.28%E2%80%AFPM.png Home A digital grid of colorful fractal patterns and charts, progressing from simple to complex as they move downward and to the right. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/522088a8-f344-4da6-80ca-faa0180b938f/Screenshot+2024-12-29+at+10.47.15%E2%80%AFPM.png Home A colorful, pixelated chart with columns labeled with letters and numbers, featuring various colored blocks with alphanumeric codes, possibly representing data or code segments. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/890789b8-95d5-4411-9005-4b92e4bdcde2/Screenshot+2024-12-22+at+12.58.08%E2%80%AFAM.png Home A colorful abstract digital pattern with vertical stripes in green, red, and blue, composed of small circular and dot elements. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/ca7f1655-1fc1-4257-a07d-5edae12c0afb/N+mod+M+Rainbow.png Home A cyclical heatmap titled 'Cyclic Heatmap of K % Modulus Values with Rainbow Colors (Original Values)' showing a matrix of numbers from 0 to 19 across 20 rows and 20 columns. The colors range from red to purple, representing different modulus values. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/70c5fe85-a828-434a-882f-750517cc1274/HueXHue_BlendModes_1.png Home Six colorful color blending and comparison charts showing different blend modes: Add, Subtract, Multiply, Screen, Difference, and Exclusion. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/08a8e36d-3761-40d6-a459-9c78dfd054f3/Brock_Algebra_kvalue_e%5Ee%5EiTheta.png Home Four scientific graphs displaying complex mathematical functions and relationships, each with color-coded data points, legends, and axes labeled with variables and units. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/aad102f1-cf64-49bd-93f0-084dc7075b75/BATrigPhase+e%5Ee%5EiTheta.png Home A set of four graphs demonstrating complex exponential and trigonometric functions. The top left and right plots show x and y components of a parametric function with cosine, sine, sine squared, and a beverage abbreviation labeled 'bro'. The bottom left plot is a parametric plot of (sin) overlays, displaying complex numbers colored by their categories. The bottom right plot shows the magnitude of the exponential of complex angles, illustrating a parabolic curve. https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/51a45ae0-460d-43b4-81c8-01a52e318537/Code_Generated_Image.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1756079645003-IMPZFRXFGZBRRSAGVGR3/BrockJNash_bedrockAsKeyArt.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/92d64e5e-de0c-4e79-99d2-58f108b39aee/%E2%89%85%E2%88%86%C2%B2%E2%81%B9%E2%81%B4%E2%88%80%E2%8C%93%E2%89%A415_%E2%87%85%5B%E2%80%A2%5D+%F0%9F%8E%A8%5B%E2%88%A0%CE%B3%5D+%E2%A7%AE%5BOv%280.40%29%5D_BJN.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/24db69c2-43cb-4bce-b9e7-46872ce85df3/x%25y%28Wrapped%29_b%28%5Bobject+HTMLInputElement%5D%29_swq%28%7B9%2C8%2C7%2C6%2C5%2C4%2C3%2C2%2C1%2C0%7D%29_r%28%C2%B11000%29_1850x1456_BJN.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/9b08dac9-3708-4642-9578-d745c20c045b/Integer%2BFractionalSwap_Vortex_Warp_b%2810%29_swq%28%7B9%2C8%2C7%2C6%2C5%2C4%2C3%2C2%2C1%2C0%7D%29_r%28%C2%B10.0001%29_BJN+%281%29.png Home https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/9ee85fcf-5665-44d9-b087-cc903d4b745b/_x_y_y%28Wrapped%29_b%2810%29_swq%28%7B9%2C8%2C7%2C6%2C5%2C4%2C3%2C2%2C1%2C0%7D%29_r%28%C2%B190500%29_1652x1611_BJN+%281%29.png Home https://www.brocknash.com/donate daily 0.75 2025-10-21 https://www.brocknash.com/equationbuilder daily 0.75 2025-09-17 https://www.brocknash.com/triangles daily 0.75 2025-09-19 https://www.brocknash.com/brocksoperator daily 0.75 2025-09-17 https://www.brocknash.com/unicode-glyph-builder daily 0.75 2025-09-03 https://www.brocknash.com/unicode-modifier daily 0.75 2025-09-03 https://www.brocknash.com/hexadecimalcolormap daily 0.75 2025-08-19 https://www.brocknash.com/sinusoidsvsparabolas daily 0.75 2025-08-22 https://www.brocknash.com/multibrotscroll daily 0.75 2025-09-17 https://www.brocknash.com/homotopy-explorer daily 0.75 2025-09-24 https://www.brocknash.com/varyrangedequationgraphs daily 0.75 2025-09-17 https://www.brocknash.com/homotopy-ref daily 0.75 2025-09-20 https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e47b4ab6-6025-4791-a099-5fef8d54d81f/ImageGallery_20250920_045813.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/66d4e7ed-9b31-4afb-ab8e-5a2c8dafca73/ImageGallery_20250920_045803.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/21b80f5e-263b-45b8-89f2-42802741a384/ImageGallery_20250920_045751.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/174206f7-e1f4-481e-9980-e7a8fe6460b2/ImageGallery_20250920_045741.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/25dc8c1a-6fc0-4236-900d-4a9fe46c2c02/ImageGallery_20250920_045734.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/8fc28db7-01a7-4f0c-8ca8-27bf9f186530/ImageGallery_20250920_045725.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/b0dab268-1e7b-46de-b8bf-ffc52055f82e/ImageGallery_20250920_045718.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/2b2ea8e1-54b2-4c64-ac69-dea009f706ce/ImageGallery_20250920_045709.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/72c56f90-1e97-45ba-a3e8-bd02b895054f/ImageGallery_20250920_045658.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1f9c8740-dd3b-43bf-b1f1-b67ae16e54a1/ImageGallery_20250920_045649.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e8d7bdde-6802-4a8a-8c7c-a94120303813/ImageGallery_20250920_045640.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/bb95bf59-3a30-45cd-84bd-5e36bfb04a62/_stack_ImageGallery_20250920_045630.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/55562485-2ce0-442d-a10a-f4dc49f32806/ImageGallery_20250920_045620.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/895929e0-41b8-4625-bb63-609b291ef3d7/ImageGallery_20250920_045611.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/5ebf2c9a-4820-40b3-a2da-aa8709a60771/_stack_ImageGallery_20250920_045558.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/13da4fcf-36d0-47ee-a7ff-cf81645e32d1/ImageGallery_20250920_045548.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/ae29c2cb-0cc3-4336-b029-b016e1f5732a/ImageGallery_20250920_045539.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/7c4d884c-e50f-4a1c-9bee-512fa99b0a4f/_stack_ImageGallery_20250920_045528.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/dacb575c-a45e-4507-b257-05f8cb52f4a5/ImageGallery_20250920_045520.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/0a0d5076-4673-4424-8683-4eb769bd86d6/ImageGallery_20250920_045512.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/5c3dc71d-9f3e-4d56-9810-6e63e0962bd1/ImageGallery_20250920_045506.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/358844b2-1adb-4ac8-be32-355d88eae27c/ImageGallery_20250920_045457.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/fdf366cf-aa57-414d-a8dd-499db5c65db4/ImageGallery_20250920_045449.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e0909b8d-9d29-4618-8d3f-a09c2fa827ee/ImageGallery_20250920_045438.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/d51b4c88-b057-4b87-984f-da3abda416dc/ImageGallery_20250920_045428.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/d1e20e14-be78-453b-bc4a-179dbb68fbdb/Sin0_ImageGallery_20250920_045423.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/79eef127-dee3-4638-8cda-4403748fad92/ImageGallery_20250920_045402.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/843e1d40-4730-43c3-b35d-fd772d5cad5a/ImageGallery_20250920_045355.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/752b8b0c-1446-4d6c-9658-b9a67c6a621e/ImageGallery_20250920_045347.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e869d8b8-ee96-47f3-8fb1-7bf2f079f99c/ImageGallery_20250920_045340.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/1170c86c-c8c5-4c47-bf00-78876829b74b/ImageGallery_20250920_045332.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/df2822b8-1a76-42dd-a953-85813030c9e3/ImageGallery_20250920_045323.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/387f4f03-57e6-4a7e-a1e0-e5881796d869/ImageGallery_20250920_045315.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/ccfacfd2-9f1e-41fc-8ed1-63ca93d8fb79/ImageGallery_20250920_045305.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/e438933d-51ae-488d-8b48-571443ed5fdb/ImageGallery_20250920_045257.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/765672aa-a128-432e-a273-73a4eb6f1da1/ImageGallery_20250920_045250.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/04702050-e219-4b43-8a35-35108a0cdc31/ImageGallery_20250920_045240.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/006c0cfd-2cb4-4b6d-8fda-03f3d188be2c/rat_combo_ImageGallery_20250920_045210.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/ffd7dcfb-9186-4f04-b005-462853a3bfa8/quartic_shift_ImageGallery_20250920_045147.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/04938ca8-1494-4c68-9074-fd789b223997/Mulit_ImageGallery_20250920_045130.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/40234330-bda4-43cc-b275-e43a194711e5/ImageGallery_20250920_045057.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/78272941-5fe2-4da2-bda1-03c8b857c4f8/ImageGallery_20250920_045046.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/bf87e19f-0201-4f9a-b25b-14c554d59e58/ImageGallery_20250920_045038.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/31df56ec-2b6f-4d3a-918a-a53521fd176e/ImageGallery_20250920_045028.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/80a567c7-633e-4a3d-8be5-a03136725178/Inv_quartic_ImageGallery_20250920_045004.png Homotopy Ref https://images.squarespace-cdn.com/content/v1/680437d9e2a0b76194d51373/8f1b59c4-f152-48fd-b40a-ddc65e44e6f4/harmonic+sum2_stack_ImageGallery_20250920_044942.png Homotopy Ref 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