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Grapher
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Grapher
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Grapher
Stable release
2.7
Operating systemmacOS
Part of a series on
macOS
History and architecture
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Applications
Utilities
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Grapher is a computer program bundled with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes a variety of samples ranging from differential equations to 3D-rendered Toroids and Lorenz attractors. It is also capable of dealing with functions and compositions of them. One can edit the appearance of graphs by changing line colors, adding patterns to rendered surfaces, adding comments, and changing the fonts and styles used to display them. Grapher is able to create animations of graphs by changing constants or rotating them in space.

History

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Before Grapher and Mac OS X, Mac OS 9 was bundled with Pacific Tech's Graphing Calculator, a similar program to Grapher that had been included with over 20 million Macintoshes since 1994 with System 7. No versions of Mac OS X prior to Mac OS X v10.4 included a bundled graphing calculator application. On July 22, 2004, Apple bought Arizona Software's "Curvus Pro X," and renamed it “Graphing Calculator”, before deciding on “Grapher”. The news was publicly announced on September 15, 2004 at AppleInsider.[1]

Version 2.0 of Grapher was bundled with Mac OS X v10.5, and version 2.1 with Mac OS X v10.6. It was notable for being one of the few applications bundled with 10.6 to ship without 64-bit support.[2] As of OS X 10.9, it became a 64-bit application.

Features

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Grapher is a graphing calculator capable of creating both 2D graphs including classic (linear-linear), polar coordinates, linear-logarithmic, log-log, and polar log, as well as 3D graphs including standard system, cylindrical system, and spherical system. Grapher is a Cocoa application which takes advantage of Mac OS X APIs. It also supports multiple equations in one graph, exporting equations to LaTeX format, and comes with several pre-made equation examples. It is one of the few sophisticated graphing programs available capable of easily exporting clean vector art for use in printed documents, but exporting 3D graphs to vector is not possible. Animation of graphs is also supported in both 2D and 3D, generating a QuickTime file.

It is also possible to use the operating system's copy-and-paste feature to copy equations from the application's visual equation editor. By doing so, Grapher functions as something of an equation editor; the user may copy images, EPS, PDF or LaTeX versions of entered equations into other applications. Any equation can be entered and copied; it is not limited to plottable equations.

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Grapher

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Grapher is a graphing calculator application developed by Apple and bundled with macOS since version 10.4 Tiger, released in 2005, enabling users to create interactive 2D and 3D visualizations from simple and complex mathematical equations. It serves as a native tool for students, educators, and professionals to plot functions, explore parametric curves, vector fields, differential equations, and series data directly on the Mac platform. The app features an intuitive interface where users can input equations manually or via templates, incorporating symbols and elements from an Equation Palette for precise . Grapher supports advanced functionalities such as animating graphs to demonstrate dynamic changes over time, evaluating equations at specific points, and performing numerical integrations. Users can customize graph appearances, including backgrounds, colors, and axes, and export visualizations as images or copy equations for use in other applications. Originally evolving from earlier Mac OS graphing tools and incorporating elements from third-party software like Curvus Pro X, Grapher has remained a lightweight, free utility integrated into the macOS Utilities folder, praised for its high-quality rendering and ease of use in educational and analytical contexts.

Introduction

Overview

Grapher is a application developed by Apple for macOS, capable of creating both 2D and 3D visualizations from mathematical equations. Bundled with the operating system since Mac OS X 10.4 in 2005, the app's core role centers on transforming equations into interactive graphs that users can manipulate and explore on screen, supporting a range of functions from basic plots to complex surfaces. This distinguishes Grapher from standard calculators, which prioritize numerical evaluations and computations, by emphasizing visual interpretation and dynamic adjustments to better illustrate mathematical concepts. As of macOS Sequoia (version 15, released in 2024), Grapher remains pre-installed in macOS as a utility tool at version 2.7, unchanged since at least macOS Monterey (2021).

Core Purpose

Grapher is designed primarily for students, educators, and professionals who require a straightforward tool for graphing mathematical equations without relying on external software. It enables users to visualize functions and data sets efficiently, serving as an accessible entry point for mathematical exploration on macOS devices. The application supports the graphing of complex functions, including parametric, polar, and implicit equations, which facilitates educational demonstrations and scientific analysis of intricate relationships. For instance, parametric equations allow for the representation of dynamic paths, such as , while polar and implicit forms aid in depicting curves and surfaces that are challenging to express in Cartesian coordinates. This capability makes Grapher particularly valuable for settings and research previews where quick iterations enhance understanding. As a free, pre-installed application bundled with macOS since version 10.4, Grapher emphasizes accessibility to promote math and learning across Apple ecosystems. Its intuitive interface bridges the gap between basic calculator applications and more sophisticated software like Mathematica, offering powerful visualization without a steep or additional costs.

History

Predecessors

The primary predecessor to Grapher was the , developed by Ron Avitzur in collaboration with Pacific Tech and Greg Robbins. This software originated from Avitzur's earlier work on graphing tools dating back to 1985, evolving through projects like Milo before becoming a standalone application in the early . Apple began bundling with its systems starting in 1994 alongside , specifically as a demonstration of the new PowerPC processor's capabilities in the original computers. The inclusion was part of Apple's strategy to showcase hardware performance by distributing select third-party applications for free, with highlighting the processor's speed—reportedly up to 50 times faster than on previous 68k-based systems—and integrating 3D for rendering. Over its lifespan, it shipped on more than 20 million machines, underscoring its role in promoting Apple's transition to PowerPC architecture. Key features of Graphing Calculator included 2D and 3D plotting of equations, along with animation capabilities for visualizing mathematical concepts, such as dynamic graphs resembling an animated blackboard for educational purposes. However, it was designed for classic Mac OS environments, including System 7 through Mac OS 9, and lacked native support for the emerging Mac OS X framework. As Apple shifted to Mac OS X in 2001, Graphing Calculator was phased out, requiring emulation via the Classic environment for continued use, which highlighted the need for a modern, native replacement built with Cocoa technologies. This transition paved the way for Apple's acquisition of Software's Curvus Pro X in as a direct bridge to Grapher.

Acquisition and Initial Release

On July 22, 2004, Apple acquired Curvus Pro X, a Cocoa-native graphing application developed by Software, a Swiss company, to bolster its suite of built-in utilities for Mac OS X. The software, originally designed for creating 2D and 3D visualizations of mathematical equations, was rebranded as Grapher and integrated directly into Mac OS X 10.4 , marking Apple's first native graphing tool for the modern operating system. Grapher's inclusion in Tiger was previewed during Apple's keynote at Apple Expo Paris in September 2004, where demonstrations highlighted an updated graphing calculator capability as part of the upcoming OS enhancements. The full release of Mac OS X 10.4 Tiger, bundling Grapher, occurred on April 29, 2005, providing users with a free, high-performance tool for scientific visualization. The initial version of Grapher offered native support for both 2D and 3D graphing, an integrated equation editor for inputting complex formulas, and export capabilities to formats such as PDF and EPS, enabling seamless sharing in professional and academic contexts. This acquisition and launch were motivated by Apple's aim to modernize its scientific toolkit following the transition from Classical Mac OS, effectively replacing legacy applications like the original with a contemporary, OS-native alternative that aligned with Cocoa's .

Version Updates

Grapher was first bundled with Mac OS X 10.4 Tiger in 2005 as version 1.1. Version 2.0 arrived with Mac OS X 10.5 Leopard in 2007, providing improved equation handling and visualization tools. Version 2.1 arrived with Mac OS X 10.6 Snow Leopard in 2009 and remained a 32-bit application. The application reached version 2.7 with macOS 10.9 Mavericks in 2013, its last significant update, which incorporated subtle user interface refinements and corrections for high-resolution displays to enhance rendering clarity. Since 2013, Grapher has not received further version increments and remains at 2.7 across subsequent macOS releases, including up to macOS Sequoia 15 in 2024 and as of November 2025, preserving its bundled status with reliable but no additional features. It continues to be bundled consistently since its origins, ensuring seamless integration in macOS utilities. On ARM-based Apple Silicon Macs, such as those with M-series chips introduced from 2020 onward, Grapher operates stably via Rosetta 2 translation without necessitating native updates, maintaining full functionality despite its Intel-era codebase.

Features

2D Graphing

Grapher enables users to create two-dimensional visualizations of mathematical functions through a straightforward interface that supports a variety of plot types, including Cartesian, polar, logarithmic (such as log-log and semi-log scales), parametric, and implicit functions. These capabilities allow for the representation of explicit equations like y=f(x)y = f(x), polar forms such as r=θr = \theta, parametric curves defined by x(t)x(t) and y(t)y(t), and implicit relations like x2+y2=1x^2 + y^2 = 1. To begin, users select File > New and choose a 2D graph type, after which equations can be added via the Add button. Equation input in Grapher uses a syntax based on standard , where functions like y=sin⁡(x)y = \sin(x) or polar equations like r=θr = \theta are entered directly into the equation field. For complex expressions, an Equation Palette is available under Add Elements, providing access to exponents (e.g., x2x^2), roots, Greek letters (e.g., θ\theta), and operators to facilitate precise entry. Multiple equations can be overlaid on a single pane by repeating the addition process, enabling comparisons such as plotting y=sin⁡(x)y = \sin(x) alongside y=cos⁡(x)y = \cos(x). Pre-built templates, accessible via New Equation From Template, offer starting points for common scenarios like parametric curves (e.g., x=cos⁡(t)x = \cos(t), y=sin⁡(t)y = \sin(t)) or inequalities. Customization options enhance the clarity and aesthetics of 2D graphs, with tools for adjusting axis scaling, including range limits, mark intervals, and positioning to suit linear or logarithmic views. Labels and text captions can be inserted via Object > Insert Text, formatted with fonts and positioned interactively, while colors and line styles for curves are modified through the Inspector panel or Format > Recolor Selected Curves, supporting selections of multiple elements with Command or Option keys. Grids are configurable under Format > Axes & Grids to aid readability, and backgrounds can be set to uniform, gradient, or other styles for professional presentation. These features allow multiple plots to coexist on one graph pane, with individual customizations preserving distinct visual identities. The same equation input methods extend briefly to 3D graphing for consistent across dimensions.

3D Graphing

As of macOS Sequoia (version 15, released 2024), Grapher supports a variety of 3D plot types, enabling users to visualize complex mathematical functions in three dimensions. The primary plot type is the explicit surface, defined by equations of the form z=f(x,y)z = f(x, y), which generates continuous surfaces representing the function's output over a specified domain in the xy-plane. Parametric surfaces extend this capability by allowing definitions through vector-valued functions, such as x=ucos⁡vx = u \cos v, y=usin⁡vy = u \sin v, z=uz = u, where parameters uu and vv vary over defined ranges to create shapes like helicoids or mobius strips. Grapher supports plotting in cylindrical and spherical coordinates through parametric equations, facilitating representations of rotationally symmetric or radial functions. Vector fields are also supported via specialized equation templates, displaying directional data as arrows emanating from points in 3D to illustrate phenomena like flow or electromagnetic forces. Equation support in Grapher's 3D mode emphasizes multi-variable functions, with the application parsing implicit dependencies and rendering updates in real-time as equations are edited. For instance, the ripple surface equation z=sin⁡(x2+y2)z = \sin(\sqrt{x^2 + y^2})
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